AFC Wimbledon chief executive Erik Samuelson has called for Milton Keynes to drop the word Dons from their name.
MK Dons were formed after the original Wimbledon club, having gone into administration, were in 2003 relocated over 50 miles north to Milton Keynes and bought by Pete Winkelman's consortium, before being renamed in June 2004.
AFC Wimbledon were formed by supporters in response and have since been promoted five times to reach npower League Two.
They will meet MK Dons for the first time on the weekend of December 1 in the FA Cup second round, after both clubs came through first-round replays.
Winklelman remains as chairman of the Milton Keynes club and Samuelson told Sky Sports News: "If he offers me his hand, as long as it's got a letter in it saying that they agree that what they did was wrong and that they're going to drop the name Dons, I'll shake it. Otherwise I think we'll just move on.
"It's up to them. I think it reminds them and everybody of how they originated. They really don't have much to do with Wimbledon but it's their decision, not mine.
"I'm not going to agitate for it, I think it would be the better thing to do but that's for them to decide."
The two clubs almost came face to face at the same stage of the competition two years ago, only for Stevenage to beat MK Dons in a first-round replay.
There were reports on that occasion that AFC Wimbledon may boycott the fixture but Samuelson insists that was never a possibility.
He said: "We're owned by fans and have regular meetings of fans, and they're entitled to put forward anything they like. A few said we shouldn't play them and we explained that if you enter a competition then you abide by the rules, and that means playing whoever you're drawn against.
"It was very short-lived and I don't think it would ever amount to anything. It was certainly never a club policy, or even a proposed club policy.
"A fair number are saying they are not going to go as a matter of principle, and that's a personal decision. Those of our fans who do go, I would think, will be very vocal indeed.
"Emotions are running very high and it's reminding everybody of how we started. Our job is to get the game played and over with - and hopefully win.
"This is a chance to show the footballing world just how proud we are of what we've achieved."