The veteran forward will be out of contract at the end of next month with Atletico Madrid and Barcelona are in the market to bring in a striker in the summer.
The 35-year-old had a successful spell at the Nou Camp and is hopeful that the Catalan giants want him back this summer.
Steven Gerrard wants to bring his former Liverpool team-mate to Villa Park as he seeks to add more experience and a winning mentality to the squad.
Aston Villa are prepared to table an offer for him, but it has been claimed that Suarez is still waiting to hear from Barcelona.
The Uruguayan may want to wait and see whether he gets an offer to move to Barcelona next season.
He could only consider offers from other clubs once he is certain that Barcelona will not be offering him a contract.
Aston Villa remain keen but they will face competition from clubs in Italy and Spain for Suarez.
Sevilla and Inter are also interested in him and want to offer him a contract ahead of next season.
