The former All Black's five-year spell at Twickenham Stoop is due to end next spring and Quins are eager to retain their most influential player.
Evans' value was underlined in last Saturday's astonishing 42-40 victory over Wasps, when he inspired an astonishing revival upon his 100th Aviva Premiership appearance.
At 32 he knows his next contract is likely to be his final big pay-day, but hints he would like to remain with Quins if the terms are agreeable.
"Both sides are in talks at the moment and it's something we want to organise early because that suits both parties," he said.
"I'm no spring chicken, but I'd also love to stay. We'll have to wait and see what happens.
"I have a few options and staying at Quins is one of them.
"I've been away from New Zealand a while, but I do love London.
"I have a great time here and work really well with Quins. The company's awesome and we have a good time.
"I will not go back to New Zealand to play. I've had my time there. If I was to move, it would be to France or Japan."
Quins will resume their title defence against London Welsh tomorrow night having spent the week addressing the defensive frailties that enabled Wasps to establish a 40-13 lead at Twickenham on Saturday.
Only the greatest comeback in Premiership history - spearheaded by a 22-point haul from man of the match Evans - rescued a seemingly impossible situation.
"I've been in a few games where we've been down, but nothing like that before," Evans said.
"I looked at the scoreboard and it was 40-13 and thought we were beaten, let's just try to keep it under 50.
"As a team we're getting ourselves in situations we've never been in before and that's a good thing
"It bodes well for the future, although we don't want teams to build up that sort of lead again."
Welsh marked their Premiership debut with a 38-18 defeat by Leicester last Sunday, underlining the challenge that lies ahead this season.
Evans, however, insists Quins have become a marked team and can ill-afford to show any complacency.
"We won the title so every side will be gunning for us now," he said.
"I remember last year when Saracens were champions that was the game we really wanted to lay a marker in.
"Teams will want to do that against us this year and that's a pressure we can use to our advantage.
"We don't expect to be given any quarter and we know we must be on top of our game in every game, no matter who we are playing
"But in the four years I've been here this is the best I've felt about this team.
"We haven't had to recruit too much and we've got another level of experience on last year.
"After winning the Amlin Challenge Cup and Premiership, we know our game inside out.
"But we must keep working. We didn't meet our targets in defence or attack last year, but it was our discipline that really let us down.
"We must improve on that so that we keep getting in positions where we can win trophies."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.