Wilder has spoken previously about his appetite to fight the 25-year-old Kiwi, but it now appears he is in a hurry to get it done.
Wilder returns to action on February 25, defending his title against Poland's Andrezj Wawrzyk in Alabama. It's his first fight since breaking a hand in a successful defence against American Chris Arreola in July.
The feeling has been that Parker will look to get a defence against a British opponent - most likely Hughie Fury - and if he comes through that, then look at bigger options like Wilder who has previously eyed a mid-year clash with the New Zealander.
But Wilder, 31, is pumped after hearing that Parker is keen to fight him. The Bronze Bomber, unbeaten over 37 fights with 36 knockouts, is now super-keen to get it on.
"When I heard that I immediately called my people and said if all goes well with this fight I have in February, I have no injuries and my hand is healed and can take 100 per cent impact on it as well, then I want that fight (Parker) next," Wilder told 78SPORTSTV
"They are talking about fighting in April and I'd love to come back and fight again in April.
"At lot of fighters wouldn't do it, come straight back ... but I want to make a great impression in 2017.
"If all goes well with this fight, I wouldn't mind turning right around and coming back and fighting Joseph Parker to unify the division with his WBO belt and my WBC belt, and do it that way.
"It's easier said than done of course and boxing is a business, there are going to be a lot of rules and regulations for that match to get it to happen.
"We are going to see what happens, but we are going to take a stab at it. They say they want it, I definitely want it."
Wilder's trainer Jay Deas has previously spoken of his fighter being willing to travel to New Zealand to fight Parker.
Parker is currently having an extended break since winning the WBO belt against Andy Ruiz in Auckland last month, though continues to work on his fitness while holidaying in New Zealand. He is targeting an April return to action and will train in Las Vegas in the buildup
If Parker's handlers at Duco Events don't want to go down the British route yet, the US market is a viable option through Wilder who is America's leading heavyweight and has a profile there.
Duco have a new working relationship with leading American promoter Bob Arum of Top Rank and he will certainly be able to pull some strings in the United States to make a Parker-Wilder fight both attainable and attractive.
Wilder is also seen as a target for the winner of the Anthony Joshua v Wladimir Klitschko fight in London in April which will have the IBF and WBA belts up for grabs.
Like all of the top heavyweights in a rejuvenated division, Wilder has options right now and it's about making the best decisions in terms of risk and reward.
Parker is similarly placed and Duco have to weigh up a schedule that could allow Parker to get more experience – and useful pay cheques – against rushing into a juicy unification bout.
At 2.01m and with plenty of experience to go with his power, Wilder would represent the biggest challenge of Parker's young but successful career than now stretches to 22 wins in a row
As for the Joshua v Klitschko fight, Wilder said it represented a "big leap" for unbeaten British fighter Joshua, the IBF champion.
"In my heart I'm going for Joshua but in my head I'm going for Klitschko. It's an intriguing fight," Wilder told 78SPORTSTV.
Meanwhile, Britain's David Price, another UK option for Parker, is keen to keep busy as he waits top see how the title race unfolds.
He will meet the WBO's European champion, Romania's Christian Hammer in London on February 4.
Photo: Photosport (Trainer Kevin Barry and his WBO champion Joseph parker are still to announce who the Kiwi heavyweight will be fighting in his first defence of the world title).