Rafa Benitez's side are currently in negotiations with Albion over the potential signing of Baggies striker Salomon Rondon, and the West Midlands club are looking to bring Gayle to the Championship on a separate deal, according to the Newcastle Chronicle.
Benitez does not want to exchange the 27-year-old for Rondon as the Newcastle manager is looking for an additional forward on top of Gayle to create strong competition for places alongside Spanish forwards Ayoze Perez and Joselu.
Yet the Magpies have instead offered Rolando Aarons on loan to the Baggies as part of the Rondon deal, and while Darren Moore has rejected taking the 22-year-old winger from St. James' Park, the offer remains open for the Championship side.
Gayle has struggled to find goalscoring form in the Premier League, despite making his top-flight debut in 2013. In his four seasons as a Premier League player - three at Crystal Palace and the 2017/18 campaign with Newcastle - the 27-year-old has only accumulated 21 goals.
This contrasts massively to his form in the Championship, as Gayle hit 13 second-tier goals for Peterborough United in the 2012/13 season, while he also led Newcastle to the 2016/17 Championship title, finding the net 23 times during that campaign.
Rafa Benitez's team will need to sort out their transfer business quickly, as the Premier League season starts in two-and-a-half week's time when the Magpies take on Tottenham Hotspur on 11th August.
Albion, meanwhile, kick-off their Championship season a week earlier, with a home tie against Bolton Wanderers on 4th August.