According to The Telegraph, Gerrard has two games to save his job following their disastrous start to the campaign. They travel to Fulham on 21 October, before taking on Brentford at home three days later.
Villa are currently in 16th place in the Premier League table, which is the same position they were in when popular gaffer Dean Smith was sacked 12 months ago. With the team scoring just seven goals and conceding 13 after 10 matches, Gerrard's days at the club appear to be numbered.
The Telegraph report states that Aston Villa are preparing an ambitious swoop for Pochettino, who is at the top of their managerial shortlist. The 50-year-old has been out of work since his departure from PSG, following a disappointing run in the Champions League.
Pochettino was a huge success in English football with Southampton first and then Tottenham, the latter of which he guided to the 2019 Champions League final. Aston Villa are also investigating the possibility of recruiting another former PSG boss Thomas Tuchel, who left Chelsea in August.
The two elite coaches will be on the shortlist if the Villans decide to part ways with Gerrard, with Villarreal manager Unai Emery also being considered by the club's hierarchy.
Steven Gerrard acknowledges job at Aston Villa under threat
Following Aston Villa's 2-0 home defeat to Chelsea, boos rang around Villa Park, with the club winning just two of their first ten top-flight games this season.
After the full-time whistle, Gerrard, who left his job at Rangers to manage the former European champions, admitted that the pressure would build on his position.
He told reporters (via The Mirror):
"I'd be stupid not to be aware of where we're at and accept that. I won't hide from the criticism. I was aware of all the shouts which came from behind the bench, but I don't think all of them were directed at me from a personal point of view. I heard a group singing from the Holte End, I'm aware of it all."
Gerrard added that the he will try everything to change the situation at the club:
"I have to accept it and try to do everything I can to change the way they are feeling. If the players can replicate the first hour of this performance, they won't have an issue."