Newly promoted Fulham, however, also has interest in the Ghanian forward and are hoping that London would be his preferred destination.
Newcastle United struggled for goals in the 2017/18 season with Dwight Gayle only managing to score six and Joselu even less with four.
Newcastle also brought in Islam Slimani on loan midway through the season from Leicester City in the hope of adding goals to his side, but after only playing four games, it didn't quite go to plan.
It's clear that Rafa Benitez is searching for a proven striker to bolster his squad. and add goals as he prepares for the new season.
Fulham is also in search of a proven forward going into the new season with Aleksandar Mitrović returning to Newcastle after an impressive loan spell in which he scored 12 goals in 17 games.
With the future of Mitrović uncertain, Fulham is considering alternatives with reports (via footballghana) suggesting the London club have made a £8m bid for Ayew that has been turned down by Swansea paving the way for Newcastle to make an improved offer.
Jordan Ayew was one of the bright sparks in a poor season for Swansea who was relegated on the final day of the Premier League season.
It's likely that Ayew will leave the Swans in pursuit of Premier League football, as was the case last season when he arrived after departing relegated Aston Villa.
The Ghanian forward scored 11 goals in all competitions, winning his clubs Golden Boot, Best Goal of the Season and Player' Player of the Year awards.
Swansea City value Ayew at £13m, and it remains to be seen who will capture his signature.