The Bhoys snapped up Matthews from Cardiff City back in 2011, and the Welsh international has racked up 150 appearances for the club during his four years in Glasgow.
Now though, Matthews' time could be up. The Daily Mail report that Celtic have accepted a £2m bid from Premier League side Sunderland, with Matthews set to travel down to Wearside for talks over the move.
However, the report also states that, despite signing Manchester United right back Saidy Janko on Wednesday, Ronny Deila's men weren't actually looking to sell Matthews, and wanted to keep him at Celtic Park.
Yet the player's desire to move on to a new challenge this summer and play in the Premier League means that Celtic have reluctantly accepted the bid from Sunderland, with the 23-year-old expected to complete the move in the coming days.
Best move for all
Celtic may have wanted to keep Matthews at the club, but it makes good business sense for the Bhoys to cash in on a player who allegedly wants a move back to English football.
With Janko signed up and Mikael Lustig also at the club, manager Ronny Deila has a number of right backs still at the club even if Matthews does leave, and that £2m can go towards Celtic's pursuit of a new striker this summer.
Matthews gets his move to the Premier League that he so wants, and Celtic can cope without him - so this move could be the best for all involved.