Hearts boss Jefferies spent five years in charge of the Bairns and almost eight in the Killie hotseat.
He knows one of them will definitely be relegated at Rugby Park on the final day of the bottom-six season tomorrow and insists he will be equally upset whichever of them does down.
Asked who he would be backing, he said: "You've put me right on the spot."
Jefferies, who left Falkirk for his first spell as Hearts manager in 1995, added: ""I had a lot of great times at Falkirk.
"I even thought about staying there - that's as big a compliment as I can pay.
"There's still a lot of people at that club I'm connected with, people behind the scenes who you never hear or see.
"You always get a great welcome when you go there.
"It's the same at Kilmarnock: you cannot spend eight years at a place and bring in players and know all the people around the scene (and not feel it).
"It will sad for whoever goes down, so I'm going to sit on the fence on that one and just say, 'Let the best team stay in the league on the day', because that's what it's down to."
Jefferies left Killie in January after falling out with chairman Michael Johnston over the amount of cutbacks being made at the debt-laden club.
He expects even more belt-tightening if they go down but is confident Scotland's oldest professional club will not go bust.
"The chairman's come out this week and said it wouldn't finish them," he said.
"I've worked with him and know how tight money was, so it's going to be huge, huge.
"It just means they'll have to make probably more and more cuts.
"But I think that'll be the same for Falkirk.
"Any team that's gone down has had to do that.
"That's why most of them struggle to come back in the one year."
Source: Team Talk
Source: Team Talk