The 25-year-old, who can also play left wing-back, has had a tough couple of years with two knee injuries and Pilgrims boss Steven Schumacher has said that he can leave permanently or on loan.
Cooper, who still has another left on his contract, has made just three appearances since December 2020 and it is thought a fresh start is exactly what he needs.
After joining on loan from Peterborough United, he played a big part in helping Plymouth win promotion from League Two in the 2019/20 season, assisting an impressive 12 goals from left wing-back.
Cooper then joined the Home Park club on a permanent deal for an undisclosed fee in September 2020, penning a three-year contract.
As well as playing for Peterborough and Plymouth, Cooper came through the academy at Crewe, making more than 100 appearances and scoring 15 goals, which led to Posh paying a fee for him.
He made his Crewe debut aged 17 and was awarded the EFL LFE Apprentice of the Year for League One.
Boss Schumacher told Plymouth Live in May: "I spoke to George and we both decided it's probably best for him to move on. He has had a tough time with injuries over the last couple of years.
"He hasn't really enjoyed it the last 18 months. It has been hard. I think it's important that he goes away now and has a fresh start.
"Fitness-wise he's okay. He's working and he's running. He's up to speed, if you like, he just now needs a good pre-season in a change of scenery, change of environment, where it will suit him.
"If he's not playing down here it can be tough because you are away from home. Maybe he will move somewhere closer to home. He will be available to either go on loan for a year or probably on a permanent somewhere else."
Schumacher added: "We are on the same page. It wasn't one of them where we fell out or anything like that.
"He just said he needed something different, we both agreed, and he's going to speak to his agent and we will put his name out. I'm sure it won't take him long to get fixed up because he's a good player."