‘The Cat’, 38, ran into the 33-year-old boxer in Italy at Bare Knuckle Fighting Championship's inaugural event in April, and Parker admitted Usyk “laughed off” his advances for a match after his upcoming spat with Daniel Dubois.
Speaking with SunSport, Parker said: “I saw Uysk in Italy, and I walked up to him and said, ‘Hey, you got two fights left. Why don't you fight Dubois and fight me?’
“He just laughed it off. He didn't really reply.”
Parker added Usyk was possibly “looking for the bigger and sort of financial-making fights” by looking to complete his trilogy fights with Tyson Fury and Anthony Joshua, whose promoter Eddie Hearn recently said could be entering the final stages of his boxing career.
Parker said: “And then now, I'm seeing that he's calling out Tyson and Joshua for his last fight in his career.
“Maybe he's looking for the bigger and sort of financial-making fights. I'm not quite sure.”
Parker is poised to face the winner of Usyk’s rematch with Dubois - which will take place on 19 July at Wembley Stadium, London - as he's he mandatory challenger for the WBO heavyweight title.
Even so, the boxer is not resting on his laurels.
He said: “I know [Queensbury Promotions head] Frank Warren said a few things that I might be next to fight for undisputed unification. But there were no discussions. And for me, it's just words at the moment.
It'd be nice to get something in writing and to get something solid. But at the moment, it's just words.
“If it can happen, I'll be over the moon.”
Last month, Warren confirmed Parker would get back into the ring in September with the winner of the Usyk-Dubois match.
He told talkSPORT: “I spoke with Joseph and his team and he will fight again in September. We will then wait and see the outcome of the rematch between Usyk and Dubois.
“The WBO have said that the winner of that fight will have to do their mandatory. He is the interim champion so he is in a good position, as he can fight for the four belts.
“Or if the winner vacates, then he will be elevated and become a full world champion.”
