The Government say they have no plans to change policy on arrivals from red list countries or force Premier League clubs to let players travel for World Cup qualifying matches in those areas.
FIFA president Gianni Infantino has written to Prime Minister Boris Johnson to request exemptions for players due to play in red-list countries during the upcoming international break.
But the Government have told Sky News that public health is their top priority and concerns over foreign variants mean there is no way the rules can be relaxed for professional footballers.
Downing Street say this is different from Euro 2020 - when all the players were contained within specific bubbles and there was less travel involved.
The Premier League announced on Tuesday that nearly 60 players from 19 clubs would not be released next week to fly off to World Cup qualifiers in 26 countries on the UK Government list.
La Liga are also backing their clubs' decision not to release players for qualifiers in countries where the players would have to quarantine on their return.
Returning to England from 'red-list' countries
The Government states those returning to England from a country on their red list must quarantine for 10 full days in a managed quarantine hotel and take a coronavirus test on or before day two and on or after day eight of quarantining.
But Infantino said in a Wednesday statement: "We have faced global problems together in the past and must continue to do so in the future.
"The release of players in the upcoming international windows is a matter of great urgency and importance."
Infantino called "on a show of solidarity from every member association, every league and every club, to do what is both right and fair for the global game".
He added: "Many of the best players in the world compete in leagues in England and Spain and we believe these countries also share the responsibility to preserve and protect the sporting integrity of competitions around the world.
"On the issue of quarantine restrictions in England, for players returning from red-list countries, I have written to Prime Minister Boris Johnson and appealed for the necessary support, in particular, so players are not deprived of the opportunity of representing their countries in qualifying matches for the FIFA World Cup, which is one of the ultimate honours for a professional footballer.
"I have suggested that an approach similar to that adopted by the UK government for the final stages of the Euro 2020 be implemented for the upcoming international matches.
"Together we have shown solidarity and unity in the fight against Covid-19.
"Now, I am urging everyone to ensure the release of international players for the upcoming FIFA World Cup qualifiers."
The Confederation of African Football [CAF] has asked the British Government to grant an exemption for African players for the upcoming window.
Their statement read in part: "CAF has noted the current circumstances in place in Britain regarding the lack of sporting exemptions for players returning from several African countries after the international window next week.
"CAF notes that similar exemptions were granted by the British Government to enable the attendance of delegations and officials, amongst others, at the finals of the European Championship held less than two months ago.
"CAF has appealed as a matter of urgency, to the Football Association and the British Government, that the same treatment previously applied to Europe now be extended to Africa under the principles of solidarity and equal treatment."
Argentina, Brazil and Egypt are among the nations currently on the UK Government's red list regarding travel to England.
The Premier League decision means Mohamed Salah would not be able to play in Egypt's World Cup Qualifier in Cairo against Angola on September 2 - and the Egyptian FA had said Liverpool had already informed them Salah will not be available.
Brazil host Argentina in a World Cup Qualifier at the Maracana on September 5, but the Premier League's decision means numerous players will miss that match, and several other big games in South America.
Eight Premier League players were named in the upcoming Brazil squad, with Liverpool trio Alisson Becker, Fabinho and Roberto Firmino joined by Ederson and Gabriel Jesus (both Manchester City), Thiago Silva (Chelsea), Fred (Manchester United), Richarlison (Everton) and Raphinha (Leeds United).
Alisson told Sky Sports News: "Honestly, I feel bad, because I want to play for my national team, I want to play for Liverpool.
"I don't want to get punished to take a decision.
"But, from what I know, it's not even a decision, and we cannot choose too much in this moment."
Aston Villa and Argentina goalkeeper Emiliano Martinez, who started in the 1-0 Copa America final win over Brazil last month, will likewise be prevented from playing his nation's qualifiers.
EFL follows Premier League approach
The FIFA president's statement was released just minutes after the English Football League announced it was following the Premier League's stance on players heading to red-list countries.
A statement read: "EFL clubs have today taken the collective decision not to release players for international matches that are to be played in countries on the UK Government's 'red list' next month.
"The EFL supports the decision of its clubs and is aligned with the position taken by our Premier League colleagues, who are also significantly impacted by this situation.
"The approach has been necessary as a result of FIFA's policy change whereby clubs are now required to release players to countries that are on a Governmental red list, where previously there was an exemption."
The Premier League statement had read in part: "Extensive discussions have taken place with both the FA and the Government to find a solution, but due to ongoing public health concerns relating to incoming travellers from red-list countries, no exemption has been granted.
"If required to quarantine on return from red-list countries, not only would players' welfare and fitness be significantly impacted, but they would also be unavailable to prepare for and play in two Premier League match rounds, a UEFA club competition matchday and the third round of the EFL Cup.
"This period takes into consideration 10 days of hotel quarantine on return to England but does not include any additional time that would be required for players to regain match fitness."