The former Liverpool striker has been rumoured to be on his way out of Atletico Madrid after 16 months with the club.
Suarez, whose contract expires in the summer, is thought to be keen on a reunion with his former Liverpool teammate, Steven Gerrard.
While Villa are yet to make an official bid for the forward, it is believed that Suarez has turned down opportunities elsewhere in order to secure a move to the West Midlands.
The Uruguayan spent four seasons at Anfield with Gerrard where he scored 82 goals in 133 appearances.
His departure from Liverpool to Barcelona came in 2014 where he would go on to win four La Liga titles and the Champions League.
A move to Villa Park would see Suarez also reunite with his former teammate, Philippe Coutinho, who joined Gerrard’s side on loan earlier this month.
If Villa are able to sign Suarez before deadline day then that could complete one of their most memorable transfer windows in the Premier League, with Lucas Digne also joining the club from Everton last week.
Ollie Watkins and Danny Ings currently have a combined total of nine league goals so far, so the arrival of Suarez - who netted 21 goals during the 2020/21 campaign - could be exactly what they need.