Midfielder Paul O'Shaughnessy and striker Gareth Seddon have also left Gigg Lane as Barrow apparently prepares to start recruiting new talent.
The Gigg Lane manager must have thoughts about the players he wants to bring in, but Shakers' fans will have to be patient to see who he has lined up as replacements.
For Clegg though, it is time for pastures new, and the 23 -year-old former Manchester United youngster is confident he can find a first-team spot at another club.
"I sent a few letters out to clubs, so I'll just have to wait and see what happens," said Clegg, who is currently holidaying in Wales with his family. "I'd like to stay in the north west because I live here with my family, but it depends what interest there is in me."
Clegg admitted he was "very disappointed" not to have been kept on at Gigg Lane for next season, but holds no grudges against Barrow.
"At the end of the day, it's all about opinions,and every manager is different," added Clegg.
"I've got nothing against Graham.
"He was great with me while he was the assistant manager.
"However, now he's the manager and he has a budget for the players he wants to bring into the club.
"I was injured for the first half of the season, but I thought I'd done quite well at the club. But I've got to move on now and try to find a new team.
"I had three great years at Bury, the fans were brilliant, so it would be nice to come back one day to say thank you to them all.
"I've still got a lot of good friends at the club - Matty Barras, Danny Swales and others. So I wish them the best of luck."
As well as trying to secure a new deal, Clegg is also looking forward to the birth of his second child with his girlfriend Sharon.
"I've just had a bit of time off since I've been released and spent that time with my family," he said.
"I'm sure the new baby will keep me busy.
"I have been trying to stay as positive as I can since I have left Gigg Lane.
"I was half expecting it to happen, but you never know in football, that's the way it goes sometimes."
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