Swansea manager Brendan Rodgers hopes that Dorus de Vries and Angel Rangel will soon sign new deals, but the offers will not be on the table forever.
The pair will both be out of contract this summer, however, Rodgers is hopeful that they will not follow Darren Pratley in snubbing extensions.
Rodgers has been delighted with the development of both goalkeeper De Vries and right-back Rangel, and he wants them as part of his Premier League squad.
The Swansea boss told the South Wales Evening Post: "I hope Dorus will sign a new contract because he is very important to us.
"He has been given a really good offer by the club and the Premier League is where he wants to play his football.
"He also wants to play for a team who allow him to express his qualities, which we do, so I'm hopeful that financially we can sort out a deal that keeps him here. Dorus is a key member of our group."
Rodgers added with regard to Rangel: "It's the same sort of situation with Angel as it is with Dorus.
"He has come from being a lower-level player in Spain and, after an outstanding season, he has the chance to play in the Premier League.
"He is out of contract so he has every right to look at his options, but we are hopeful that we can keep him.
"We have given him a good offer and we're hopeful that he'll stay and play for a team who suit him and in an area where his life is good. Hopefully the whole package will allow us to keep him."
Rodgers, though, does not want either contract situation to drag on and act as a distraction.
"I will not let it go on too long, but I have to respect that they need thinking time," said Rodgers.
"They understand that the deals will not be on the table forever - they have to make a choice because we have to move forward."