Promoter Frank Warren has told Gennady Golovkin to "sign the contract" within the next 10 days if he wants to fight Billy Joe Saunders this summer.
Warren intends to match Briton Saunders with an alternative opponent if a deal is not reached to face the world's leading middleweight by the end of next week.
Warren has already made an offer for Saunders to face Golovkin in his homeland of Kazakhstan on June 10, but is yet to hear back.
Saunders (24-0, 12 KOs) holds the WBO belt -- the only version of the world title that Golovkin (37-0, 33 KOs) does not hold.
California-based Golovkin, 34, says it would be "a dream" to face Saunders and Warren says there are no objections from Saunders about travelling to Triple G's homeland, where he has not fought since 2010.
"We've been in talks for a long time and it's time to put up or shut up," Warren told ESPN.
"We thought we had a deal in place before the [Danny] Jacobs fight but then the WBA ordered a mandatory defence against Jacobs.
"Golovkin says his dream is to hold all the belts, well we can make his dream a reality. All he needs to do is sign the contract. Wherever and whenever they want. Billy is a traveller by name and nature so will fight him anywhere - Kazakhstan, America or England.
"But we're not going to keep waiting. If something is not done in the next ten days we're going to have move on.
"Financially the terms have been agreed and it's just whether they want to do it or not."
Golovkin -- recently promoted to ESPN's pound-for-pound No. 1 boxer -- defended his WBC, IBF and WBA belts via a unanimous points decision of 115-112, 115-112 and 114-113 over American Jacobs (32-2 29 KOs) on March 18, which ended Golovkin's 23-fight knockout streak.
A fight between Golovkin and Saul 'Canelo' Alvarez is being considered for September, but hopes for that much-anticipated showdown happening were not helped by the 170,000 pay-per-view numbers on HBO in the U.S.
Before then, Alvarez (48-1-1, 34 KOs) faces fellow Mexican Julio Cesar Chavez Jr (50-2-1, 32 KOs) in their catchweight fight (at 164.5 pounds) at the T-Mobile Arena in Las Vegas on May 6.
Saunders, 27, has had a dismal time as champion so far. After impressively out-pointing Irishman Andy Lee for the belt in December 2015, injuries have restricted him to one appearance since then -- a points win over Artur Akavov last December, when he was lucky to hold on to his title on points.