Steven Gerrard and Roberto Martinez are on Aston Villa's shortlist of possible replacements for Dean Smith.
Villa are expected to speak to at least five or six managers - or their representatives - as they narrow down their search for a successor, having sacked Smith on Sunday following a run of five straight Premier League defeats.
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Both Gerrard and Martinez are in work, at Rangers and Belgium respectively, so Villa know they would have to pay compensation.
Martinez is open to the possibility of a move back to the Premier League, having been with Belgium since 2016, during which time he has taken them to No 1 in the FIFA rankings.
The Spaniard was offered the job 10 years ago by Villa's former owner Randy Lerner but he opted to remain in charge of Wigan Athletic at the time.
Gerrard, meanwhile, is a close friend of Villa CEO Christian Purslow following their time together at Liverpool when Purslow was managing director.
Denmark boss Kasper Hjulmand is also on the list of possible names and he is well known by Villa sporting director and fellow Dane Johan Lange, but is seen as an outside option at this stage.
Villa's bosses want a new head coach in position in time for the game against Brighton a week on Saturday, but will take their time to assess their options now there is an international break.
Smith said on Monday he was confident he could have got the team back on track after injuries to key players, while lauding his record at Villa Park of having got them promoted back to the top flight in his first season, kept them up the term after, and then steered them to an 11th-placed finish in 2020-21.
Via the League Managers' Association, he said: "I believe those achievements allowed the club to accelerate its ambitions to become an established Premier League club.
"My belief was that we would continue our progression this season. I understand the football industry and, of course, I respect the owners' decision, but I felt that with important players soon returning to full fitness we would achieve a top-half finish."
Villa also confirmed the departure of assistant head coach Craig Shakespeare on Monday.
'Would Rangers let Gerrard go? And for how much?'
Sky Sports News reporter Rob Dorsett:
"Martinez of course has been Belgium boss since 2016, taking them to world No 1 in the FIFA rankings, but I understand he would be interested in potentially coming back to a management job in the Premier League.
"Steven Gerrard is a more difficult one because he's in place at Rangers doing a very good job there. So, would Rangers be prepared to let him go? How much compensation would they demand? Is Steven Gerrard interested in coming back?
"We know that Gerrard is a close friend of the Villa chief executive Christian Purslow. The two men worked very closely together at Liverpool when Purslow was managing director there from 2009.
"We also expect the Denmark manager Kasper Hjulmand to be on that list. He's a close friend of Johan Lange, the Aston Villa sporting director.
"So, there are plenty of names in the frame now for Aston Villa. I expect them to narrow that down over the next few days as they speak to either these candidates or their representatives, but the news we can bring on Sky Sports News is Roberto Martinez and Steven Gerrard are very much on Aston Villa's shortlist as possible replacements for Dean Smith."
Jamie Carragher says joining Aston Villa would be a "great move" for Gerrard - but ideally he would win a second league title in Scotland first.
Carragher said: "I think Aston Villa as a club would be a great move for Steven Gerrard. But the situation he finds himself in right now is that he took the title away from Celtic last season, and he's in a great position to win it again. I think in a perfect world you'd want to stay at Rangers to the end of the season and come away from there with two titles.
"I mean, this is not something coming from Steven Gerrard but, 'I look I've been in a job for four years in the Scottish Premiership', and I think sooner or later there's going to be a great chance Steven Gerrard is going to come to the Premier League. But for me, it's a difficult one.
"If he got offered the Aston Villa job, I don't think there'd be many jobs in the Premier League which he would get offered better than that. People talk about Liverpool, and that might be another two or three years with Jurgen Klopp but you're not going to get any better jobs, so it would be a decision for him.
"But, in a perfect world, I think Steven Gerrard wants to come away from Rangers with another couple of trophies."
Sky Sports' Gerard Brand:
Aston Villa were ruthless in the summer transfer window in attempting to replace Jack Grealish, spending nearly £100m on Emi Buendia, Danny Ings and Leon Bailey. They have shown a similar ruthless edge in sacking Dean Smith after five straight defeats.
Under owners Wes Edens and Nassef Sawiris and chief executive Christian Purslow, it is clear backwards steps will not be tolerated.
On top of the five defeats, Villa's performances were concerning. In those 450 minutes, they played well for an accumulative hour, but 40 points gained from their last 36 games will be the real reason for Smith's sacking.
There are plenty of mitigating factors, but Smith cannot escape blame for all.
November 20: Brighton (H)
November 27: Crystal Palace (A)
December 1: Man City (H)
December 5: Leicester (H) - live on Sky Sports Premier League
December 11: Liverpool (A)
December 14: Norwich (A)