Promoter Eddie Hearn has warned James DeGale and Lee Selby their careers could lose momentum if they box more in the United States than at home in Great Britain.
Hearn wants super-middleweight DeGale and featherweight Selby to make second defences of their IBF world titles at London's O2 Arena on April 9. Both have their careers guided by powerful American boxing advisor Al Haymon and are waiting to learn when they will make mandatory defences of their titles.
The pair last fought on the other side of the Atlantic and are due back in action in late March or April.
"April 9 at the O2 Arena is a perfect home for both of those fights but we are running out of time because we are building up that card already," Hearn told ESPN.
"Al Haymon will have his strategy and if they want to come to the UK I will promote it and if they don't, I will co-promote it and it will be shown on Sky from the USA.
"I don't have the same involvement with them as I did before, but I would really like to see Lee Selby and James DeGale fight over here next because if they continue to box in North America they may as well forget about the UK market.
"They will lose momentum if they don't fight next in the UK, but unfortunately it's not up to me, it's up to the fighter.
"Boxing at 5am in front of a smaller audience on TV is not doing you any favours, when they could both be fighting at a packed out venue over here at primetime.
"It's good money over there and you can't knock it but if you are going to develop it in the UK market they have to show their faces here. There's no money in the US for their next fights so I think the UK is a good place for it."
Londoner DeGale (22-1, 14 KOs), 29, is due to face little-known Venezuelan Jose Uzcategui (24-1, 20 KOs) next after having his last two fights in America and Canada. Welshman Selby (22-1, 8 KOs), 28, will defend his belt against American Eric Hunter (21-3, 11 KOs) after last fighting in Arizona three months ago.
Hearn hopes Selby and DeGale will be part of the bill on April 9 that also includes unbeaten heavyweight Anthony Joshua (15-0, 15 KOs), whose opponent could either Londoner Dereck Chisora, American Bryant Jennings (19-2, 10 KOs) or Frenchman Johann Duhaupas (32-3, 20 KOs).
However, Hearn is less optimistic about the chances of Sheffield's IBF world welterweight champion Kell Brook (35-0, 24 KOs) and Bolton's Amir Khan (31-3, 19 KOs) facing each other at Wembley Stadium on June 4, after a Twitter row with Khan on Friday.
Hearn claims Khan's team are demanding am 80-20 split, which would give him £7 million to Brook's £2.5m, even though he would be the challenger.
Hearn says if Khan is willing to accept 60-40 in his favour, the fight can still be made. But former world light-welterweight champion Khan, 29, is hoping to face new WBC welterweight champion Danny Garcia instead. Garcia, who out-pointed fellow American Robert Guerrero on Saturday, knocked out Khan in four rounds in 2012.
Khan was at the Garcia-Guerrero fight while Brook, 29, first faces a mandatory defence of his IBF belt against Kevin Bizier on March 26 before he hopes to take on a big name in the summer.