The Netherlands centre-back has not featured in the Premier League this season, his only two appearances for the Merseyside club coming in the League Cup.
Heitinga, 30, is in the final year of his contract and would relish the opportunity to play in Serie A.
He told Gazzetta dello Sport: "There is nothing official. 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."
"There are a few Serie A teams interested in me; 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."
Heitinga moved to Goodison Park from Atletico Madrid in September 2009 and has made 114 league appearances for the Merseyside club.
