Joshua added Joseph Parker’s WBO title to his WBA and IBF belts with a points victory over the New Zealander in Cardiff last night.
The British heavyweight said after the fight that he would like negotiations for a bout with WBC champion Wilder to take place in private, adding he was “not into the business of hype”.
A match-up between Joshua and Wilder has been anticipated for some time, with the US fighter claiming he had “declared war” on Joshua earlier this year.
Barry Hearn, chairman and founder of Joshua’s promoters Matchroom, has revealed that negotiations to make the fight happen will start as soon as possible.
“It is a fight Anthony Joshua really wants and I think he wants it this year,” he told BBC Radio Five Live’s Sportsweek programme.
Joshua has said he would like the bout to take place in the United Kingdom but Hearn is not ruling out the possibility of it happening in the United States if the terms are right.
Matchroom view Joshua as a much bigger drawing card in the UK than Wilder is in the US.
Hearn said: “Anthony Joshua wants all the belts – that is the big card Deontay Wilder has got to play (but) commercially, Joshua is far bigger than Deontay Wilder.
“I think Wilder would come over here because in the world we live in, in boxing, the couple of million dollars Wilder is getting for a fight is pretty small fry in comparison to the rewards that await him for a Joshua fight.
“Travelling is not usually a problem if the money is right.
“But I still think in the long term, if Anthony sits down and thinks it through, he may come to the decision that to be a truly global sportstar he needs to go to America – not just for the money – but, in terms of the brand value of AJ, fighting in America is going to be on his horizon.
“I wouldn’t rule out AJ fighting in America despite his comments last night.”
Joshua was forced to go the distance for the first time on Saturday night, but was unanimously declared the winner as two judges scored him 118-110, while the other had him at 119-109.
After his win, the heavyweight champion told Sky Sports: “My strategy was to stick behind the jab.
“I was switched on and I was focused, Joseph Parker is a world champion I said this was about boxing finesse.
“What you can’t forget is that I am the unified heavyweight champion of the world.”
Both fighters had stepped into the ring at Cardiff’s Principality Stadium undefeated and the win extends Joshua’s perfect pro record to 21 victories from as many bouts.
More from UK
Travel delays expected as UK braced for more snow
‘Reputation matters’: Russia accuses UK of blocking its ‘right’ to see poisoned spy and his daughter
Queen congratulates RAF on reaching centenary during celebrations
British teenager arrested in Amsterdam over Essex murder
Yorkshire Three Peaks Challenge: Weary walkers offered bus ride to finish
Relief for grieving parents as the Government axes child burial fees
Joshua had won his previous 20 fights all by knockout but struggled to land clean shots on Parker.
After the fight, American heavyweight Wilder tweeted that Joshua’s victory had been a “robbery”, and posted a video the following morning in which he claimed promoter Eddie Hearn was ignoring a phone call from him.