The report claims that Leicester are looking to add more firepower to their ranks, and have identified Gayle as an ideal candidate to help them in their quest for a remarkable Premier League title triumph.
The former Peterborough United man has been on the periphery of Palace’s first-team this season, prompting plenty of speculation over his future during the current transfer window.
Alan Pardew’s side have since bolstered their squad with the addition Emmanuel Adebayor, pushing Gayle further down the pecking order and seemingly closer to a Selhurst Park exit.
Swansea have been keen admirers of the striker, with the report in the Mirror claiming the Welsh club launched a £7 million offer for his signature on Friday.
The alleged offer has yet to form into anything concrete, though, giving Leicester enough time to persuade the 26-year-old to move to the East Midlands rather than the Liberty Stadium.
Claudio Ranieri’s side are seemingly desperate to add a new striker, and after missing out on Eder to Inter Milan, Gayle represents a decent option with his pace and intensity key attributes.
Given the choice between the two, the prospect of Champions League football at Leicester must be a huge incentive although he may find playing regularly easier to come by at Swansea.