According to Wales Online, the Magpies are set to join top Turkish clubs Besiktas, Galatasaray and Fenerbahce in the hunt for Ayew's services.
Besiktas are believed to be in pole position for the player, with the deal said to be intended as a season-long loan with a view to a permanent transfer.
Rafa Benitez's Newcastle are now said to be preparing to hijack that potential move late in the day, as the Magpies continue their search for a striker.
As far as current reports stand, there is not believed to have been a firm approach for Ayew yet, but the 28-year-old Ghana international is understood to want a move away from the Liberty Stadium this summer.
The club is willing to allow the player to leave, and will not stand in the way of an exit should a firm offer arrive, with new manager Graham Potter seeking to try and move on several first-team players ahead of the new season.
Ayew struggled to find form during his second spell at the Liberty Stadium.
The forward failed to score a goal in 12 appearances following his £18m return to South Wales, and now looks set to depart the club.
Despite the poor form, Newcastle remain interested in the player as they search desperately for a source of goals ahead of the new season - their top goalscorer in the league last season being attacking midfielder Ayoze Perez with just eight.
Ayew was in good form during his first spell at Swansea, scoring 12 goals in 34 league appearances during the 2015/16 Premier League season an the Swans finished 12th.
Newcastle were relegated to the Championship that season.