The 26-year-old has not played for Schalke during pre-season after spending last term on loan in Holland with Vitesse Arnhem.
The Ghana international admitted that he will need to find a new club to play regular football this season.
He told Sky Sports News: "I have not been called up for any pre-season games, it's embarrassing.
"There has been some contact from clubs but I have two years on my contract with the German club, so we will have to see what happens."
Villa boss Paul Lambert is understood to be a big admirer of Annan and will make a formal enquiry to bring the player to the Premier League.