The report claims the Swans are keen on bringing in a new striker this month and have made an enquiry for Gayle, yet Palace are holding out for an initial £6.5 million fee rising to £9 million.
Gayle has been on the peripherals of the Palace starting eleven this season, struggling to play the lone forward role in the way which boss Alan Pardew prefers.
Palace’s recent signing of Emmanuel Adebayor is likely to push Gayle further down the pecking order, prompting plenty of questions over his future at Selhurst Park.
Relegation-threatened Swansea are seemingly desperate to add to their striking options this month and a player of Gayle’s calibre would undoubtedly be a good move for the Welsh side.
The former Peterborough United striker offers plenty of pace and mobility upfront, ideal for a side who play a possession-based game and are looking for a striker to run in behind the defence.
Swansea need more goals throughout their team, as they currently rely heavily on talented forward Andre Ayew to maintain his decent scoring record and fire them to safety.
With Palace seemingly happy to sell, a deal could be struck before the end of the January transfer window though only if Swansea, or another potential suitor, meet the London club’s asking price.