Hull would consider letting record signing Jimmy Bullard join Celtic on loan if the Glasgow giants made an approach.
Bullard is thought to be one of a number of high-earning players the Tigers are keen to offload following their relegation from the Barclays Premier League.
Hull claim Celtic are interested in the former Fulham and Wigan midfielder but the 31-year-old's injury record may deter clubs from seeking a permanent move.
Head of football operations Adam Pearson said in The Daily Express: "We are aware that Celtic have an interest in Jimmy Bullard.
"They haven't made a direct approach to me but I know officials from Celtic have spoken to a number of people on our coaching staff about Jimmy Bullard.
"Everyone is aware of our financial predicament and we would have to consider all offers.
"If Celtic were to make an offer for Jimmy Bullard, whether it be a permanent transfer or a loan deal, then it is something we have to give serious consideration to."
Bullard has three years remaining on a contract reported to be worth £45,000 per week.
Hull finished in 19th in the Premier League with debts of £35million and are anxious to cut costs to avoid administration.
Bernard Mendy this week left the club by mutual consent while the remaining players are considering a request from the club to accept a deferment of part of their wages.