Swansea have offered manager Graham Potter a new contract in an attempt to ward off interest from Brighton, Press Association Sport understands.
The Premier League club want Potter to succeed Chris Hughton, who was sacked on Monday.
Swansea rejected Brighton's approach to speak to Potter earlier this week and hope an improved deal will persuade the 43-year-old to stay at the Liberty Stadium.
Potter was appointed last summer after leaving Swedish club Ostersunds and has two years left on his current contract.
It is understood that he has sought assurances from Swansea's American owners over transfer plans this summer.
But the Welsh club remain in the process of a cost-cutting exercise following their relegation from the Premier League 12 months ago.
Swansea accept they are powerless to stop Potter leaving for Brighton if he chooses to.
Potter, who was coincidentally on the south coast on Thursday night watching the Sky Bet League One play-off between Portsmouth and Sunderland, is expected to make his decision over the weekend.
Potter built his reputation in Sweden, where he won three promotions with Ostersunds and steered them into the Europa League.
Swansea finished 10th in the Sky Bet Championship last season and Potter was credited with playing an attractive brand of football, even though financial constraints saw him lose 16 first-team squad members.
Brighton sacked Hughton the day after their campaign ended with a home defeat to champions Manchester City.
Hughton's side managed just two wins from their 18 league matches after the turn of the year and finished 17th, only two points clear of Cardiff in the final relegation place.
It is understood Brighton chairman Tony Bloom wants to appoint a new manager as quickly as possible to aid pre-season planning ahead of the 2019-20 campaign.