Chelsea are not willing to bid above £40m for Raheem Sterling, according to Sky sources.
Manchester City have tabled two bids for Sterling, the second believed to be around £40m for the Liverpool and England forward.
Sky Sports News HQ understands Chelsea are also interested in signing the 20-year-old but are not prepared to meet Liverpool's £50m valuation of the player.
Sterling joined Liverpool from QPR in 2010 and is under contract until 2017, but has turned down the offer of a new deal worth £100,000-a-week.
He has maintained throughout negotiations that his issue is not about money, stating in April, in an interview not sanctioned by the club, that he did not want to be viewed as a "money-grabbing 20-year-old".
Brendan Rodgers has insisted Sterling is not for sale, despite Manchester City's pursuit of top English talent, and plans to invest heavily.
City's chairman Khaldoon Al Mubarak said last week: "You will see us in the market bringing in high-quality individuals that fit within what we are aspiring to.
"We want a squad which is able and has the capability and quality to win the Premier League, to compete and win the Champions League and be able to go all the way in two cup competitions in England."
Chelsea, on the other hand, have discussed the possibility of letting one of their players go. Mohamed Salah is set to meet with Fiorentina to discuss extending his loan.
If he wants to stay at the Italian club they will be forced to pay £1m for his services for the year.
If he decides to stay at Chelsea they will have to keep or sell him, they would not be able to loan him out to another club due to the terms of his contract.