The 18-year-old has also been linked with a move to Glasgow Rangers, but it seems Celtic are leading the race for his signature.
The Bhoys are just waiting for Bolton’s administrators to hand over preferred bidder status.
Back in May, The Sun (12/5 page 59), reported that the Whites were considering making a move for the versatile youngster who can play as a midfielder or as a defender.
Connell is out of contract at the end of the season, and Leeds or Celtic would have to pay a compensation fee which is thought to be around £300,000.
Celtic are also expecting to confirm David Turnbull as their first summer signing in the coming days.