Hull chairman Paul Duffen has admitted that Wayne Brown may need to look elsewhere for regular action.
The defender, who featured heavily during the club's successful promotion campaign last season, has featured just once this term.
The 31-year-old has been linked with several clubs of late, with a loan move seemingly the more viable option.
Derby have dismissed reports linking them with a move for Brown, but Championship rivals Doncaster and League One outfit Scunthorpe are believed to be interested.
Duffen told the Hull Daily Mail: "Any player who can see they are unlikely to get first-team football is going to start considering their future and what is best for them.
"Wayne is a consummate professional and he has been an absolutely fantastic servant for Hull City.
"He's not the sort of player who is happy not to be playing first-team football, but at the minute he knows he's not going to get that action.
"That's no reflection on Wayne as a player, it is just a fact of life that we have brought in two excellent centre-halves.
"Wayne now looks at the competition for places and he knows Anthony Gardner and Kamil Zayatte are ahead of him in the selection process for the first team at present."
Meanwhile, another player that has been left kicking his heels on the sidelines of late is Stelios Giannakopoulos.
The Greek international is yet to feature for the Tigers since arriving at KC Stadium as a free agent in September.
He did play for an hour in a behind-closed-doors game against Doncaster on Tuesday, but remains some way off a first-team debut.
"Stelios got through 60 minutes and he looked sharp," said Hull boss Phil Brown.
"He's got a long way to go in regard to his physical condition but in terms of his mental sharpness, he looked cute.
"Coming into a new club with different demands can be difficult and it's probably going to be another week to 10 days.
"That means that West Ham (on Sunday) and probably West Brom (on 25th October) will be out of the question."