The report state that Besiktas have joined Olympiacos and PAOK in the race to sign the 29-year-old keeper.
Ochoa moved to Malaga following a string of impressive performances in the 2014 World Cup however, has made just six appearances in the Copa del Rey all season.
Ochoa came close to leaving Malaga in January but his club denied him permission to leave.
Malaga’s sporting director Mario Armando Husillos told ESPN: “He is going to stay in Malaga, there is only a little time left and I just don’t see us getting any kind of great offer nor do I see us contemplating it.
“I think he will be here, we are not going to get into any problems. In football, what you have leftover from today is never enough for tomorrow, things can change radically.”
Besiktas have also been linked with Chelsea’s out of favour keeper Petr Cech.