The Jambos have reportedly turned their attentions to the Killie boss after failing in their attempts to lure Mark McGhee away from Motherwell.
Johnston accepts he can't compete with Hearts supremo Vladimir Romanov in the financial stakes, but hopes Jefferies can be persuaded to stay.
"After Jim and Billy Brown accepted pay cuts in 2005, they were given substantially improved contracts so their position is better than it has been in the past at Kilmarnock," the chairman said in the Daily Record.
"But they are still under contract with us and I am expecting them to stay.
"We haven't received an approach from Hearts, nor would we welcome one.
"Jim and Billy are abroad at the moment so I don't think any decisions will be made over the next few days.
"Jim will be back at the weekend and I will speak to him then about this."
Jefferies already has an affinity with Hearts after enjoying a successful five-year spell at Tynecastle prior to his move to Bradford in 2005, and has made no secret of his desire to coach at the highest possible level.
"We have had this situation before. Whenever a team are looking for a manager Jim is always in the picture," he added.
"It is flattering he is always at the top of people's lists but hopefully he will be happy to stay.
"I don't think it is the first time the Hearts job has been suggested to him.