According to The Scottish Sun, McGregor is on the radar of Leicester City manager Brendan Rodgers.
Rodgers worked with the Scotland international midfielder at Celtic and wanted to sign the 26-year-old in the summer of 2019 as well, according to the report.
McGregor has been on the books of Celtic his entire professional club football career so far, and has won the league title six times with the Hoops.
Having won the Scottish Premiership title for the past nine seasons, the Glasgow giants will be aiming to make it 10 in a row during the 2020-21 campaign.
McGregor has said that he wants to stay at Celtic Park beyond the summer, and has explained why he signed a new contract in November 2019.
McGregor told The Scottish Sun: “I am loving my Celtic career and it seems to be going from strength to strength.
“I signed a long-term deal last year. That’s what I wanted, and that’s what the club wanted.
“We were desperate to get nine in a row, and now we can put all our energy into trying to finish the job by getting to ten next season.
“That’s the vision Celtic spoke to me about. That’s where they see the club going. They want Celtic to remain dominant and I want to be part of that.
“It’s why I pledged my long-term future to the club. We have done well to have this period of dominance, and we want to continue it.”
As stated on Celtic’s official website, the 26-year-old midfielder has scored 49 goals in 275 appearances for the Glasgow giants so far in his career.
McGregor is one of the best players in the Scottish Premiership, and he will be an important figure in Celtic’s quest to make it 10 league titles in a row next season.