Craig Bryson has come through the youth ranks at Broadwood

Jefferies said that the chairmen of both clubs have had discussions about the 20-year-old's future.

"We don't know if Craig can do it at this level," said the Killie boss.

"We want to give him the opportunity and trying to build a fee based on how well he does for us that would reward Clyde as well."

Interview: Kilmarnock manager Jim Jefferies

Talks between the First Division outfit and Premier League Killie had been delayed until the end of the Scottish Football League season.

Scotland Under-21 international Bryson has spent three years in the Clyde first-team after having come through the Cumbernauld club's youth set-up.

It was an honour to receive two young player of the year awards Clyde midfielder Craig Bryson

Bryson told the Clyde website: "There have been many high points in my Clyde career, starting with my debut.

"The win over Celtic was obviously one and scoring at Ibrox was another.

"The match against Manchester United was also a great occasion although I couldn't get near Paul Scholes.

"Off the park, it was an honour to receive two young player of the year awards.

"Without a doubt the low point was losing the Challenge Cup final this season.

"But I've really enjoyed my time at the club and I've been here for a good few years, so it's going to be hard to leave."

Bryson had a trial with Derby earlier this season.

He rejected a contract extension with Clyde, who will be due compensation should he leave in the summer.