The Ukrainian defended his WBC, WBA, IBF and WBO cruiserweight titles - as well as the prestigious Ring Magazine belt - with a devastating eighth-round knockout of Tony Bellew at the Manchester Arena.
There have been rumours swirling for some time that Usyk is set to step up one weight class to the more lucrative heavyweight division having seemingly beaten all foes at 200lbs.
A bout against Joshua is particularly tantalising as both fighters won Olympic gold at London 2012 and have made giant strides in their unbeaten professional careers so far.
Usyk acknowledged that he will eventually move up to heavyweight but when asked about a Joshua showdown, he said through a translator "It's too early.
"If you want to speak of this then you can speak of this but we still need to wait a little bit.
"You must be professional in taking those kinds of decisions. You need to take your time to think through everything properly.
"But becoming the heavyweight champion is not what I'm dreaming of, it's my goal, it's what I'm planning to do."
Usyk defied a determined start from Bellew and a hostile reception in Manchester to gradually get on top and prove why he is regarded as one of the finest fighters on the planet irrespective of weight class.
He closed the show in spectacular fashion, following a rapier jab with a booming left hook that put Bellew on his back and forced referee Terry O'Connor to wave the count after two minutes of the eighth round.
"I was focused and concentrated, that was the assignment given to me by my corner," Usyk said. "I had to stay focused within every single round. He is a really dangerous man, he put some strong punches in.
"I told him that he is a real man, he is the father, husband and true warrior. Those kinds of fights when a warrior meets a warrior is something that should definitely take place in boxing."
Usyk now plans to take some time away from the ring after a hectic year in which he became undisputed cruiserweight champion after winning the World Boxing Super Series.
Usyk added: "Right now my biggest concern is my rest because I want to have a vacation with my family.
"I had a really tough year, it was the most difficult year of my career. It was the most successful one but the most difficult as well."
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