Middlesbrough are the latest club to be linked with Gayle, but Norwich City are believed to have placed the 28-year-old in their list of potential transfer targets, too, while fellow newly-promoted side Aston Villa could be another option for the forward.
The Magpies will be looking to recoup in excess of the £10m they paid Crystal Palace to sign Gayle during the summer of 2016, though United hope a second-tier outfit who are looking to secure promotion next term may even be willing to stretch towards £15m.
Gayle himself is believed to be settled on Tyneside; the forward did not want to leave for West Brom last summer, and that is one of the reasons why Newcastle had to raise his salary in order to secure the bespoke loan swap for Rondon.
The forward would ideally like another opportunity to show he can translate his prolific Championship form into the Premier League, be that with Newcastle or elsewhere.
Like a significant number of other Magpies , Gayle is waiting to learn whether Benitez is going to stay on as manager, as that will play a key role in determining the future of many Newcastle players.