The Wigan Athletic manager is said to be pals with the man Celtic hired less than 18 months ago.
Doherty, who moved to Celtic in 2017 after spells at Sunderland, Chelsea and Everton, is said to be close friends with Cook.
And it is claimed the Latics manager could try to set up a reunion with his fellow Liverpudlian, who holds the position of First Team International/UK Scout at Celtic Park.
The Scottish Sun credits Doherty with having unearthed Wayne Rooney at Everton, and says it was Cook who alerted him to Seamus Coleman.
Cook was Coleman's manager at Sligo Rovers in the Everton right-back's native Ireland.
Although currently a second tier side, Wigan could offer Doherty a chance to be close to his roots, being situated less than an hour's drive from Liverpool.
How big of a blow would losing Doherty be for Celtic?