The museum was left disappointed last month after trying to buy Sir Peter's Olympic singlet at auction for $122,500, but having to pull out of the sale when the singlet turned out to be fake.
Sir Peter lives in the southern United States' city of Dallas and could not be contacted this afternoon.
But speaking to the New Zealand Herald before doubts were cast on the authenticity of the singlet, Sir Peter said Te Papa should get the two Olympic golds still in his possession.
"They don't have to pay for them, they would get them as a bonus. I've talked to my wife and she thinks it's a good idea. I just have to make sure [the rest of my family] are OK.
"I think they really belong to New Zealand. I was representing New Zealand, they made it possible. I just happened to deliver. I've enjoyed having them for all these years."
He said the donation should happen "sooner rather than later".
A keen senior sports' competitor, he was considering taking part in the World Masters' Games in Auckland next year.
That could be a good time to hand the medals over, he said.
Te Papa chief executive Rick Ellis said the museum would be thrilled to have Sir Peter's medals or other memorabilia in the national collection.
"These objects have an incredible story to tell about New Zealand's sporting history. We will continue to talk to Sir Peter about the opportunity. His generosity and goodwill are quite humbling."