The England international, who was the subject of a rejected £12m bid from the Premier League champions, had reportedly mentioned to the Toffees that he would like to join the Red Devils.
However, a move failed to materialise and since then, reports have claimed that the Merseyside outfit are poised to hold talks over a new deal.
"From having interest to a situation where you have to consider a move is very different," ESPN quotes Martinez as saying. "Leighton is a very special footballer and a special player for Everton and we are looking forward to him enjoying the challenge that lies ahead."
"When the window is open I think it's the wrong time to speak about those things and so we hadn't discussed it but, now the window is closed, we are going to look into all the players in the squad and see where their contracts are up to."
The 28-year-old's current contract runs until 2015.