Rangers are also interested in securing the services of the Irish youngster who impressed despite Bolton’s dismal campaign in the English Championship.
The club will be playing in the League One next season after relegating, and suitors are ready to pounce on Connell.
Norwich, Southampton, Wolverhampton Wanderers, Brighton and Hove Albion and Sheffield United have all been linked with the midfield sensation, while Everton and Tottenham Hotspur are also interested.
Celtic won the domestic treble for the third season running, and are aiming to win the Scottish Premiership ten times in a row having now won the last eight.
Rangers will be looking to stop them next season, and it’s no surprise that both of them want Connell as squad rebuilding continues this summer.
The teenager, who featured in just 12 games for Bolton but impressed scouts, will be available for just training compensation fees, and both Scottish giants know they can secure the services of a highly-rated teenager who has a huge sell-on value.