The 32-year-old, who will miss the next three weeks with an ankle injury, will be a free agent at the end of the season.
"There is a new contract on the table," said Quins director of rugby Conor O'Shea.
"We want him here for another three years and hopefully that will happen. We've offered him what he wants in terms of length. It's up to him now. We've put our best foot forward."
New Zealander Evans joined Harlequins in 2008.