The Dutch defender has not played in the Premier League all season and only made two appearances in the club's Capital One Cup campaign.
Heitinga has 114 Everton appearances to his name since arriving at Goodison Park from Atletico Madrid in 2009, with former Toffees manager David Moyes paying £5million for the centre-back.
However, with a lack of game-time and Heitinga appearing out of favour under Roberto Martinez, the 87-cap Netherlands international says there are plenty of offers on the table elsewhere.
"There is nothing official," he told Gazzetta dello Sport after being linked with a move to Roma. "My contract expires in June, and there are many chances for me to leave Everton.
"Roma? I heard a lot about their interest. I think we should know something more concrete next week.
"I'm waiting too. I have played in Spain and England, and I'd also try the Italian experience."
Heitinga insists he would be open to a move to Serie A and is hoping to open discussions as soon as possible.
"There are a few Serie A teams interested in me," he added. "I'm waiting for official news from my agents.
"Roma are one of the best teams there are in Italy; if the interest is serious, we'll talk for sure within the next few days."