Hull are 20th in the Championship and without a win in five in the league, which could spell the end of Leonid Slutsky's brief time in charge of the Tigers.
Assuming he's appointed, Lambert would likely arrive in time for the January transfer window, but could any of his former players follow him to the KC Stadium?
Here's three he could target...
Lambert worked with the Wolves winger at Blackburn and took him to Molineux in January this year. The versatile winger has only started once in the league this season, however, and it's hard to see Wolves putting up too much resistance should an offer materialise. Hull will perhaps be wary of losing their own winger, Kamil Grosicki.
Danny Graham (Blackburn)
A player who thrived at Blackburn after being signed by Lambert, Graham has lost his way a little since then, scoring three times in 17 appearances. A reunion with his old boss at Hull - where he spent part of the 2013-14 season on loan - could bring him back to his best. His contract expires next summer.
Callum Robinson (Preston North End)
Lambert gave the Preston winger his debut at Aston Villa and could turn to him again if Grosicki is sold in January. Robinson was linked with a move to Wolves while the Scot was in charge (Daily Mail), although he only recently signed a new three-year contract at Deepdale, where he has scored or created 32 goals in 103 games.