The Netherlands international has been told he will be allowed to leave Goodison Park after falling out of favour under Martinez.
Heitinga is eager to secure a place in his country's squad for the FIFA World Cup in Brazil and the centre-back rejected a move to West Ham earlier this month.
Roma and Galatasaray have been linked with a move for the 30-year-old, who scored in Everton's 4-0 FA Cup fourth round win at League One strugglers Stevenage on Saturday.
That may have been his last appearance for the Merseyside club, as Everton manager Martinez confirmed after the game that there has been "strong interest" in the former Atletico Madrid man.
Heitinga joined the Premier League club from Atletico in September 2009 and has gone on to make over 100 appearances, but he has found first-team opportunities hard to come by this term.
The Dutchman has only made one appearance in the Premier League this season, coming on as a substitute in the victory over Norwich City earlier this month.
