Sources close to Hitzlsperger insist the Germany international is keen to go back to the club where his career blossomed in the Premier League.
Hitzlsperger had indicated when he left Villa six years ago that he would "one day like to return to the club" and that remains the case now his spell at West Ham has ended.
A source close to Hitzlsperger said: "Thomas wants to go back to Villa. He enjoyed some great times there."
Fulham, Blackburn and Stoke are also believed to be interested in signing the 29-year-old, who has won more than 50 full caps for his country.
Hitzlsperger joined Villa from Bayern Munich's academy and became a firm fans' favourite during his five years at the club.
He was nicknamed 'Der Hammer' by Villa supporters because of his explosive shooting power which yielded several spectacular goals.
Villa report back for pre-season training on Friday and new manager Alex McLeish is looking to strengthen his squad as soon as possible.
Manchester City goalkeeper Shay Given and Wigan winger Charles N'Zogbia - whom he tried to sign when in charge of Birmingham - are amongst his potential targets.