A WBA heavyweight title fight between champion Anthony Joshua and Alexander Povetkin will be "finalised in the next 72 hours", says promoter Eddie Hearn.
Russia's Povetkin, 38, is the mandatory challenger to Joshua and a UK bout is likely to take place in September.
There would also be an agreement for a unification fight against WBC champion Deontay Wilder in February 2019 at Cardiff's Principality Stadium.
Hearn says a deal with Wilder will be done "in the next month".
The Matchroom Sport promoter said: "The Povetkin deal is virtually done. The Wilder one is not, but we are talking every day."
Joshua holds the WBA, WBO and IBF belts, while Wilder holds the WBC title and Hearn suggested a fight for all four belts could take place in October or November.
However, if no agreement is reached, then that fight "will definitely be signed" before September's meeting with Povetkin.
Hearn added: "Wilder understands he has to go where Joshua tells him to and at the moment Joshua's telling him, 'You have to come to the UK'. He knows, he is up for that, but there are a lot of things that have to be worked out."
Meanwhile, Ireland's unbeaten Katie Taylor will fight on the undercard of Dillian Whyte and Parker's heavyweight fight at London's O2 Arena on 28 July.
Taylor intends to fight despite her father being shot at his boxing gym in Ireland on Tuesday, an incident in which one man died. She has described her family as being "very distressed".