Villa boss Alex McLeish has admitted that Hitzlsperger, who is a free agent after leaving West Ham in the summer, is a player that he is interested in.
However, Villa must sell before they can buy as they try to reduce an £80m wage bill.
"Thomas’s name has been mentioned," said McLeish. "The midfield, in terms of experience, maybe we are a little bit lacking.
"But we won’t be bringing players in until we trade. We still have a very heavy wage bill and we’ve got to try and work to adjust that.
"There’s players at the club we respect totally, but they haven’t played much first-team football and we have to try to let them seek football somewhere else."
Hitzlsperger made 99 appearances for Villa during his spell at the club from 2001 to 2005.