The 26-year-old former Dunfermline striker, whose contract is up at the end of the season, scored one and made another against Hibernian at Rugby Park which gave Kilmarnock just their second Clydesdale Bank Premier League win in the last 14 games.
Jefferies said: "He says he wants to stay so we are hopeful but I am very restricted in what I can offer. It's just one of those things, if he gets an offer that I can't match then I will lose him.
"Time will tell but it certainly won't happen unless we get a massive offer in terms of cash. I will be keeping him until the end of the season and then he will be free to go.
"It shows you how hard a job it is here because then you have to find people for the budgets you have.
"Sometimes when you improve them and they do well, they are targets for others and it's very frustrating.
"He will have an agent collecting offers for him and the funny thing is it will be clubs that are a similar level to ourselves who can offer him a few hundred quid more than I can.
"But sometimes for a few hundred quid, you are better staying where you enjoy playing."
Nish played his cards close to his chest, telling PA Sport: "I've not really got any thoughts on it.
"I like it here and I want to stay but I will need to wait and see. I am trying to concentrate on my football and not speak to anybody about that.
"There is a (new) Kilmarnock contract on the table and I have still to decide what I want to do. I'm 26 now and it's quite a big decision and so I will take my time to decide.
"I will just keep my head down and work."