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Martinez confirmed in a press conference on Friday that Heitinga had been given permission to speak to "a couple of clubs", one of whom is believed to be Galatasaray and the other from Italy.
The Dutchman has just six months left on his contract but is keen for more regular action between now and May in order to boost his World Cup chances.
However, he is not that keen as he has already turned down a move to West Ham this transfer window and reports suggest he may turn down these latest moves too.
Everton are unlikely to receive much of a transfer fee for Heitinga should he leave but it would lighten the wage bill and possibly spark a return to the transfer market.
Martinez is keen to recruit a defensive midfielder to act as cover for Darron Gibson but has little leeway without a major departure.
When asked about Heitinga, Martinez said no deals were agreed but confirmed he could still leave before Friday's deadline.
Even if he stayed and potentially scuppered a deal for a midfielder, the Spaniard insists he would be satisfied with his January signings:
"He [Heitinga] was given permission to have talks with a couple of clubs and over the next 48 hours we will find out what the final outcome is.
"It is very important that in this window we try to find the right solution for him. But if that solution is to stay at Everton, he is somebody we didn't want to lose in the first place.
"If I'm honest with you, bringing Aiden and Lacina in were the big priorities for me. My focus now is on bringing the players back that we've already got.
"We've been affected by too many injuries and we are working on getting all those players back. For me, football is not about numbers, it's about quality.
"Every window we will try to be as strong as we can be. We haven't lost any of our top performers and we have added two good additions, so we are stronger. I'm really pleased with Aiden and Lacina coming in.
"What we want is to get all the players back from injury because when we have everybody fit and available we have very strong options."
What are your thoughts on Heitinga? Is it crucial he leaves and we sign a midfielder? What do you think of our transfer window business so far? Have your say below.
