The Cottagers are on the lookout for their successor to Marco Silva after the Portuguese boss agreed to join Benfica following five years in West London.
McKenna, who led Ipswich Town to promotion for the second time in three seasons, is hotly tipped to join Fulham, but there is a major stumbling block.
According to Ben Jacobs, his contract at Portman Road includes an £8 million release clause, and the London side are weighing up whether to trigger it.
Jacobs did reveal that McKenna is "keen on" joining Fulham, an established Premier League side, after almost five years in the dugout at Ipswich.
The 40-year-old has won 106 of his 222 matches in charge of the Tractor Boys and is currently preparing them for an instant return to England's top-flight.
McKenna has stayed loyal to Ipswich when he could have jumped ship previously, but it will be interesting to see whether he leaves the club if Fulham trigger his release clause.