Swansea captain Garry Monk has called on Paul Anderson and Febian Brandy to turn their loan deals into permanent ones.
Swans chairman Huw Jenkins has been in negotiations with the pair since the season finished, but progress has been slow.
Anderson's parent club Liverpool, and Brandy's employers, Manchester United, have given their respective players permission to make permanent moves to the Liberty Stadium.
Jenkins is understood to be losing patience with the youngsters as he awaits their decisions, and he has set a deadline for negotiations to be finalised before turning his attention to other transfer targets.
But team captain, Monk, is keen for the pair to make their moves permanent after they played a key role in Swansea's promotion to the Championship.
Speaking to the South Wales Evening Post, he said: "It would be great if we could get Ando [Anderson] back, but that situation is out of the club's control.
"The club can only do what it has done and give them a chance to prove themselves at a higher level.
"The Championship will be much better than League One, but if Febian comes back I'm sure he's good enough to adapt."