The Paraguay international is seeking a move away from the Etihad Stadium this season in search of first-team football.
The former Blackburn marksman finished the second half of last term back at Ewood Park, but he failed to score in nine Premier League appearances.
Santa Cruz is further down City's extensive pecking order following Sergio Aguero's arrival and he is keeping most avenues open before the transfer window closes.
The striker's father and agent Aproniano admits the Championship is a competitive division full of ex-Premier League teams with excellent facilities.
Ambitious Leicester are believed to be in the hunt for the 30-year-old hit-man along with Simon Grayson's Leeds United.
"The Championship is very competitive with powerful teams who, not long ago, were in the top division and have huge stadiums, like Leeds," Aproniano told The Sun.
"Ultimately, his future will be decided by City but Roque would consider playing for such a team.
"City are looking for another club for him because Roque wants to go to a different team where he can have more chances to play."