Steve Cooper has held talks with Andre Ayew over the Ghana international's future.
The 30-year-old ended the 2019/20 campaign as the club's top scorer with 18 goals in all competitions, 16 of which came in the Championship.
But given his hefty wages, he's expected to depart the club this summer as Swansea look to further reduce costs.
Cooper has publicly admitted that - despite enjoying working with the attacker - he feels Ayew is a player that should be operating above Championship level.
"I would like nothing more than for Andre to be playing with us again next season," said the head coach after his side's play-off semi-final defeat to Brentford.
“We have seen the real level of player he is this year, with the goals he has scored and the impact he has had on and off the pitch. It’s been brilliant to work with him.
“But I understand Andre is a better player than the Championship. That’s a matter of fact and I am sure he will have offers to do that."
It's understood Ayew has regularly attracted interest, particularly from wealthy clubs in Qatar and Dubai.
Ayew's position as captain of the Ghana national team is something he cherishes, and the striker is keen to operate at the highest level possible over the coming years in a bid to remain in peak condition for when it comes to playing for his country.
Rumours recently surfaced that French powerhouses Paris Saint-Germain had tabled a €5m bid for Ayew.
But the club are yet to receive any concrete offers for the man who returned to the club from West Ham in January 2018.
And the same applies to every other member of their first team squad.
The likes of Mike van der Hoorn and Erwin Mulder have been released while loan players including Ben Wilmot, Rhian Brewster and Conor Gallagher have returned to their parent clubs.
Others including Welsh pair Joe Rodon and Connor Roberts have been linked with moves away from the Liberty Stadium, but - as with Ayew - no bids have been received as of yet.
The summer transfer window closes at 11pm on October 5.
There will be an additional domestic window that then runs until 5pm on October 16.
