Forster spent the 2019-20 season on loan at Scottish Premiership giants Celtic from Premier League club Southampton.
The 32-year-old goalkeeper played an important role in the Glasgow giants winning the Scottish Premiership title for the ninth season in a row.
Celtic manager Neil Lennon told Sky Sports in July that he wanted to bring Forster back to the club.
Lennon said that although the Hoops and the Saints had agreed on a deal, the former Newcastle United prospect was taking his time.
Southampton CEO Semmens has now claimed that Forster did not want to go back to Celtic.
Semmens told BBC Radio Solent Sport: “There’s never been any issue with Fraser from a relationship point of view. He’s trained brilliantly, he’s a fantastic guy, and the manager and him haven’t had any issues. He’s obviously always been our player and one we watch carefully.
“Fraser made an active decision to come back. He didn’t want to stay at Celtic anymore, he wanted to come back and play for us and we’ll give him that opportunity.
“So Fraser has been a full part of the squad since he came back. He’s training and doing really well. We’ll see how that develops.”
Celtic are a massive club and Forster did well at Celtic Park last season, but it seems that the 32-year-old wants to fight for his place in the Southampton first team during the 2020-21 campaign.
It is not going to be easy for the Englishman, who will have to compete with Alex McCarthy and Angus Gunn for the spot between the posts.