Dempsey has scored 22 goals in all competitions for the Cottagers this season and came fourth in the voting for the PFA Footballer of the Year award.
However, he has just 12 months remaining on his contract at Craven Cottage and recently confirmed he does not intend to make a decision on his future until the summer.
He has been linked with a switch to Everton at the end of the season and was unable to make an impact at Goodison Park on Saturday as Fulham were beaten 4-0.
The 29-year-old has been with Fulham since 2007 and McKinlay has outlined the importance of the attacker staying with the club.
"I think it is vital to keep Clint," said McKinlay, who filled in for ill manager Martin Jol against Everton.
"He has been outstanding this season and I am sure the club will be doing everything in its power to keep him. He has been a vital player for us and, hopefully, we shall get that one tidied up."