McGregor, 22, has come up through the ranks at Celtic, but was sent out on loan for the 2013-14 season, spending time with English club Notts County, where he hit 14 goals in 40 games.
After making his first-team debut for Celtic in the summer of 2014, McGregor has been around the Bhoys squad under Deila, managing five goals in 31 games last term.
This year though, the young midfielder has really impressed, scoring three goals in 16 games, including a memorable strike in the Europa League against Ajax.
His performances have allegedly triggered interest in his signature, with The Sun recently reporting that Premier League outfit Swansea City have been impressed with him, but were put off by Celtic's £3m asking price for the Scottish playmaker.
Now though, The Scottish Sun report that Partick Thistle are lining up a shock loan move for McGregor in January, as they look to build on an impressive four-game winning run.
It seems bizarre to think that Premier League clubs are looking at McGregor and yet he could end up at Partick this season, whilst many would believe that he will be in Deila's plans.
Yet with the likes of Scott Brown, Nir Bitton, Stefan Johansen, Tom Rogic and Scott Allan all competing for places, Celtic may instead want McGregor to go out on loan again - and Partick appear to be leading the race for a loan move next month.