According to Daily Mail, the Scottish champions are currently leading the chase for the prodigiously talented midfielder.
The youngster is quite versatile and he can play as the defensive midfielder or on the left side of the midfield. He has filled in at left back as well.
The player is thought to be valued at around £240,000 and Celtic should be able to afford that without any problems.
Connell is one for the future and Celtic must look to secure his services now that he is available on a bargain. The Scottish outfit have done well to develop talented youngsters into first-team stars in the past and they will be hoping to do the same with the Bolton player.
The 18-year-old has the talent to make an impact in the Scottish League next season. Even though he is unlikely to start every game, he could be a decent squad option for Neil Lennon.
It will be interesting to see if Celtic manage to get the deal over the line now.
They need to add more depth to the side before the start of the season and Connell would be the ideal addition.
Celtic need to improve their attack and defence as well. Whether Lennon is backed in the market this summer remains to be seen.