Cullip is out of favour at Sheffield United after a fall-out with manager Neil Warnock. He's only made 11 appearances for the Blades since they paid Brighton £250,000 for him in December, and has since been out on loan at Watford.
They're not pursuing their interest in the 28-year-old though since changing managers, so the player is back on the market.
Cullip was previously Taylor's captain at Brighton, and the now Tigers boss today described him as "somebody I would always be interested in bringing to the club."
However, he deems a move unlikely due to the wages Cullip would expect.