Clyde have made an enhanced offer in the hope keeping goalkeeper Bryn Halliwell at Broadwood.
Clyde hope to conclude talks with Bryn Halliwell this week
The Cumbernauld club are anxious not to lose their second first-team player in a week.
Veteran midfielder Paul Kane retired from the game at the weekend after a season wrecked by injury.
Player-manager Alan Kernaghan will speak to Halliwell before Saturday's First Division match against Alloa Athletic in the hope of concluding negotiations after the 22-year-old rejected the club's initial offer.
The former Wimbledon goalkeeper has been regular first-choice as Clyde made a surprising but ultimately doomed bid for promotion but is out of contract in the summer.
Meanwhile, Kane had intended to retire at the end of the season but decided to stop playing with immediate effect and three months before his 38th birthday.
"I'd felt recently that I wasn't playing up to the standards I expect, that my body was telling me it was time to pack it in," he said.
Paul Kane has been struggling with injuries this season
"I'd picked up three calf injuries in the past 15 months, which was annoying as I hadn't been troubled in the previous 19 years.
"I felt my body was telling me the time had come.
"I didn't want to be remembered as a guy who'd hung around living off past glories and content to hope for a seat on the bench.
"So, rather than hang on for the end of the season, I've decided to move over and give some of the young lads at Clyde a chance to show Alan Kernaghan what they can do."
Kane's career began 20 years ago at the club he supported as a boy, Hibernian.
Spells at Oldham Athletic, Aberdeen, Viking Stavanger in Norway and St.Johnstone followed before he arrived at Broadwood.
He will, in the short term, concentrate on his new business but has not ruled out a coaching role in the future.