Gerrard is under pressure to save his job at Villa Park after a poor start to the campaign.
Following a 2-0 defeat against Chelsea, the former Rangers boss has been put under further pressure, making the next two matches against Fulham and Brentford extremely crucial.
It is believed that even if Gerrard survives a defeat against Fulham, he would need to defeat Brentford to give him a chance of continuing in his post.
And in case they decide to part ways with the Liverpool legend, Pochettino will be their number one target to replace him.
Aston Villa co-owners Nassef Sawiris and Wes Edens, together with executive chairman Christian Purslow and sporting director Johan Lange, would be involved in the process of convincing Pochettino.
However, Pochettino has spent the last six years of his management in the Champions League and therefore, would need to be convinced to join a club fighting relegation.
If Pochettino refuses to join Aston Villa, the club might turn their attention to the likes of Thomas Tuchel and Unai Emery.
