The Newcastle United striker found his opportunities limited last season – and only made eight Premier League appearances.
Gayle – whose goals got the club promoted in the 2016/17 season – has another two years left on his contract.
And the Daily Mail report that the 32-year-old is in discussions over a move to Championship club Middlesbrough.
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Gayle spent the 2018/19 season on loan at West Bromwich Albion.