Albion will offer Simon Rodger and Dean Blackwell longer contracts to stop them being snapped up by other clubs.
Boss Steve Coppell revealed: "Their monthly contracts run out in the middle of next week.
"I will be talking to both players on Monday to try and sign them on a more permanent basis, but the ball is very much in their court."
Former Crystal Palace midfielder Rodger and ex-Wimbledon centre half Blackwell have been key figures in Albion's mini-revival.
The Seagulls have beaten Bradford at home and drawn at Wolves since Coppell brought the pair into the starting line-up.
"I think they have really enjoyed playing at the club for a month," he said. "The location of the club is good for both players and, given the financial climate of football at the moment, I'm not sure whether they will get a better offer at the level we're competing at.
"I very much want them to sign for a longer period, because I think they both have a lot to give us."
Meanwhile, Republic of Ireland striker Graham Barrett's loan spell from Arsenal expires at the end of the month but Coppell is confident the Gunners will let him stay for the rest of the season.
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