Steven Naismith scored Sunday's winner against Rangers

But Rangers' Walter Smith refused to divulge whether he will be one of the bosses making the call after Naismith's goal clinched a victory at Ibrox.

Jefferies said: "If I'm being honest, I would find it very strange if we didn't get some enquiries from clubs.

"As well as the goal, the way he put himself about for the team was great."

Interview: Kilmarnock striker Steven Naismith

The 20-year-old Naismith has already had a trial at Arsenal.

And Jefferies admits he faces a tough job holding onto his prize asset at the end of the season, with the Old Firm likely to be leading the chase for his signature.

"If he had to stay here, it wouldn't be the worse thing in the world for him," he said.

Whether Steven Naismith is one of our targets or not, you are free to speculate Rangers manager Walter Smith

"He enjoys his football here, and he's only 20, so another year would be great.

"I'm going away on holiday in the summer and I'm just not going to put my phone on.

"Sometimes he is the difference between winning games and not and he showed that against Rangers."

Smith has already recruited the services of three players for next season.

Jean-Claude Darcheville will arrive on a two-year deal from Bordeaux in the summer, while St Mirren's Kirk Broadfoot and Alan Gow from Falkirk have signed pre-contract agreements.

Asked whether Naismith is likely to join the list, Smith said: "We are looking for a number of players and we will try to bring a few in.

"Whether Steven Naismith is one of those or not, you are free to speculate."

However, Smith has backed Andrew Shinnie and Steven Lennon to keep up the pressure on the senior strikers at Ibrox.

The manager insists he will keep 17-year-old Shinnie and 19-year-old Lennon - who together helped the youth team to a league and cup double - in his plans.

Both came off the bench in the second half of Saturday's 1-0 home defeat by Kilmarnock in the Scottish Premier League, with Lennon catching the eye.

"He looked very lively," Smith told Rangers World, "and he's been getting a number of goals for the under-19 team and they've been doing very well.

"It's good that they can get that opportunity to come in and get a taste of first-team football.