Briton Tony Bellew and Ukrainian Oleksandr Usyk both say they are "ready" to fight each other.
Usyk, 31, became the first man to hold all four world cruiserweight titles - WBO, WBC, WBA and IBF - when he beat Murat Gassiev on Saturday to win the inaugural World Boxing Super Series.
After the fight, Bellew tweeted: "Usyk I was born ready. Let's get this done."
The Olympic 2012 gold medallist, who has won all of his 15 professional fights, replied: "I'm also ready."
Bellew, 35, has beaten compatriot David Haye at heavyweight in his past two fights, and his promoter Eddie Hearn says talks about a fight against Usyk will take place this week.
"Tony has felt fantastic up around the 15st weight and I'm not sure he will make cruiser again but I know with Usyk's desire to move to heavyweight it certainly wouldn't be a deal-breaker," he told Sky Sports.
In his first column for BBC Sport - prior to Usyk's meeting with Gassiev - Bellew spoke about his next fight.
"I love the sound of a Tyson Fury fight. I like the thought of gaining revenge over WBC light-heavyweight champion Adonis Stevenson, who beat me in 2013. If I face him and win, I'd have beaten every man I have ever fought in a ring," he said.
"I do like the thought of fighting Andre Ward and I know he has not retired properly, he's still in the gym. And finally, there is the winner from the Oleksandr Usyk and Murat Gassiev World Boxing Super Series cruiserweight final on Saturday.
"That bout, with all the world cruiserweight belts on the line, would be my number one choice in a heartbeat if all of the options paid the same pot of money. The sad fact is they don't."