The Lions ended Steven Gerrard’s reign at Villa Park on Thursday night after Aston Villa went down to a damaging defeat away at Fulham in the Premier League.
They are now moving quickly to try to bring in a replacement for Gerrard and have set their sights on Pochettino.
The Argentine tactician has now been approached by Aston Villa about taking up the vacant managerial post.
However, it is suggested the feeling from those around Pochettino is that he will wait for other opportunities and pass on the Aston Villa job.
Villa face a tough task changing his mind and it remains to be seen what they can offer the former Paris Saint-Germain coach to tempt him to take the post.
Pochettino was strongly linked with the job at Manchester United before Erik ten Hag was appointed by the Red Devils.
The Argentine has regularly managed in the Champions League in recent years, along with fighting for silverware, and he would be walking into a relegation scrap at Aston Villa.
