The Welsh outfit’s new boss Graham Potter has made a left-sided central defender his top priority and head of recruitment Kyle Macaulay travelled to Pittodrie on Thursday to watch the 21-year-old in the 1-1 draw.
The Swans’ Championship rivals Hull City failed with a £1million bid in January and Dons boss Derek McInnes won’t want to lose McKenna, especially with central defender Mark Reynolds out of action.
The 31-year-old has undergone knee surgery and has been ruled out for up to seven months.
The reported £10m price tag Aberdeen slapped on McKenna after he signed a five-year contract back in March may prove problematic for Swansea.
Former Dons youth coach Neil Cooper believes it will take an “outstanding offer” to prise McKenna away from Aberdeen.
“English clubs probably think Scottish sides need the money because we don’t generate as much cash through TV deals as they do,” said Cooper.
“Derek McInnes is in the driving seat with McKenna’s deal so if a club wants to buy him they’d need to make an outstanding offer for the club to consider it.
“It’s a credit to the club’s youth system that Scott is playing for Scotland. McInnes is experienced enough to know that if he loses a player of his quality what his valuation is.”
Kyle Bartley’s departure to West Brom and the lingering questions over the future of Alfie Mawson have put Potter in a tricky situation defensively as he looks to get his squad in shape ahead of their opening Championship fixture at Sheffield Utd on 4 August.