Swansea boss Paulo Sousa is keen to tie Leon Britton and Garry Monk down to new contracts at the Liberty Stadium.
Britton is close to agreeing new terms and Sousa is hopeful skipper Monk will follow suit.
Swansea have recently agreed new deals with Ashley Williams and Alan Tate and Sousa is determined to keep his best players.
"I hope we can resolve things with Leon, probably this week or next week," Sousa told the Evening Post.
"Garry is another player we want to keep and there are some more we want to speak to. Some of them have two years left on their contracts already but we are looking to extend those deals.
"By doing that we give them some recognition for their work and we show them what we expect from them now and in the future."