Evans, who is out of contract with Quins next summer, has reportedly attracted the attention of a number of French and Japanese clubs.
"I will not go back to New Zealand to play. If I was to move, it would be to France or Japan," said Evans.
"I have a few options and staying at Quins is one of them. Both sides are in talks at the moment and it's something we want to organise early because that suits both parties.
"I'm no spring chicken, but I'd also love to stay. We'll have to wait and see what happens."
Evans was named the players' player of the year in the 2011-12 season.