The Sun says the Hoops hope to name Howe as their new boss this week - but he may not take charge until the summer.
Talks are continuing over a deal to appoint the former Bournemouth gaffer as Neil Lennon's successor.
An official announcement is NOT expected in the next 24 hours with both parties reluctant to rush negotiations.
Howe, 43, has verbally agreed in principle to accept the job offer from Celtic.
But, crucially, he wants certain assurances, as well as being allowed to take his trusted ally Richard Hughes with him.
Celtic are looking to name a new director of football as well as a head of recruitment - and Howe is pushing for Hughes to be lured away from his role at Bournemouth.
The Hoops hierarchy are believed to be open to the idea, but it would mean ripping up plans they were already putting in place.
Manchester City's Fergal Harkin was one of the names in the frame.
Howe's desire to work with Hughes has complicated the talks.