An enthralling fight in Los Angeles ended in a draw, although many ex-professionals said Briton Fury should have been declared the winner, BBC Sport reported.
"I've got a funny feeling he's going to get his running shoes out and stay away from me," said Fury, speaking on ITV.
Wilder's trainer Jay Deas told BBC Radio 5 live he wants a rematch.
After the 12 rounds – during which Fury was knocked down twice – the fight was scored 115-111 for Wilder, 114-112 for Fury and 113-113, with Alejandro Rochin the judge who had the American as the winner.
Briton Fury, 30, said he had "never seen a worse decision in my life" and described it as a "gift" for his 33-year-old opponent.
"I should have been rewarded with the decision and be taking the WBC belt back to Britain but, unfortunately, it stays in America. We both stay unbeaten and we've got to roll the dice again," added Fury.
Deas said he would want Wilder to take on Fury again before a potential fight with IBF, WBO and WBA champion Anthony Joshua.
"If it's something that people would like to see again we would absolutely love to do it. Both the guys put on a tremendous fight," Deas added on Monday.
"If it was up to me – and only me – I would like to do the Fury fight first because I think there is unfinished business.
"If the money makes sense in the UK I would love to do it there. Deontay has never had a problem with travelling. That's not the issue at all."
Fury's promoter Frank Warren said he and the British Boxing Board of Control will write to the WBC demanding another bout.
"You'd think they'd want the rematch. They've said they do," said Warren, who suggested the contest could be in March or April.
"It's got a good chance of coming to London. You'd have a 90,000 gate at Wembley, so you're talking serious money.
"But with Tyson, he'll travel – he'll go where the money is."
Several former world champions, including Floyd Mayweather, Lennox Lewis, Tony Bellew and Carl Froch, believed Fury should have won.
He was floored in the ninth and final rounds, meaning they were scored 10-8 in Wilder's favor.