The Finland international Eremenko - who struck four goals during a year-long stint in Ayrshire three years ago - was paraded at half-time during the 2-0 win over Inverness.
"I don't know how close we are yet but I will speak to Alexei later," said the Killie boss.
"Obviously we are interested in quality players and it would be great to get him here.
"Time will tell whether we can afford him but it is a positive that we have got him here to talk. It doesn't guarantee anything so we will have to wait and see."
With six days left of the January transfer window, it is the thought of seeing top-scorer Boyd - again on the scoresheet against Caley Thistle - leave that is giving Johnston cause for concern.
"It was a real team performance but there was also some really good individual performances," he added.
"Robbie Muirhead was great, while young Gregg Kiltie was fantastic too starting his first game. He took the ball in tight spaces and was never afraid to play a pass.
"The young players did so well but without the experience of Boydy and Sammy Clingan that result wouldn't have been possible.
"We cannot afford to lose somebody like Boydy. He is too big a player for us with his goals."
Inverness manager John Hughes said: "We huffed and puffed, we had a few chances of our own - but it wasn't meant to be. we're better than that.
"We had a great standard last week, and we fell below it - it's very disappointing."