The Bhoys seem to have identified the former Bournemouth boss as the man to take charge of the club as their new manager.
Howe is interested in the job and talks have taken place between the club and the manager, but he is not rushing into conversations and wants to take his time before agreeing to take the job.
It has been claimed that the 43-year-old has expressed an interest in bringing his previous club Bournemouth’s technical director Richard Hughes with him as the director of football.
Celtic are interested in appointing a director of football and Howe has suggested Hughes.
But concerns have been raised inside the club and Celtic are in two minds about agreeing to appoint Howe’s man.
The Scottish giants see their next director of football as someone who will shape the long-term vision of the club.
The director of football is also the man who plays a role in managerial appointments and Celtic are concerned about Howe bringing in his own man for the job.
The Bhoys are also worried that if Howe leaves in two or three years’ time, Hughes could also leave with him.
Celtic want to avoid the situation that saw Brendan Rodgers take Lee Congerton with him to Leicester City.