City boss Roberto Mancini has said the Paraguay international is surplus to requirements at Eastlands and can leave in the January transfer window.
The 29-year-old, who came off the bench against Birmingham on Saturday for just his second appearance of the season, has been linked with Wolfsburg, Fulham and Leicester.
City are thought to have offered Santa Cruz to Steve McClaren's Wolfsburg as part of a swap deal for Bosnian striker Edin Dzeko, as they did with Craig Bellamy over the summer.
But Dzeko has committed himself to the Bundesliga club for the rest of the season while Santa Cruz's agent Jan van Baal claims Wolfsburg have not expressed a desire to take the former Bayern Munich man back to Germany.
"I am not aware of the interest of Wolfsburg," he told the Daily Express.
"They are not interested in the player."
Santa Cruz has suffered an injury-hit spell at City since making a £17.5million move from Blackburn in July 2009 and, when fit, his first-team opportunities have been limited by the form of Carlos Tevez and Emmanuel Adebayor.
He has scored three goals in 20 Premier League appearances for the Blues, although only six have been starts.
Source: Team Talk
Source: Team Talk