Celina has spent the last four years at City, but the 21-year-old has only made one start and three substitute outings for the Premier League giants.
However, the attacker has enhanced his reputation during loan spells with both FC Twente and Ipswich Town, and it now appears that a Championship club are prepared to sign the Kosovo international on a permanent basis.
According to the Manchester Evening News, new Swansea boss Graham Potter is prepared to spend £4m to add Celina to his squad ahead of the new campaign.
Celina netted seven goals in 35 appearances at the second tier with Ipswich, and it appears that Potter views the wideman as one of his priority additions.
The Welsh outfit's only first-team signing this summer is Joel Asoro, who has arrived at the Liberty Stadium from Sunderland.