The 31-year-old has struggled with injury over the last few years and relegated Hull are understood to want to offload him due to his high wages as they look to restructure financially. Pearson says he will not stand in the player's way if he is interested in the move.
"We've told Celtic we'd be willing to let Jimmy go out on loan and it is now up to the player. Jimmy is currently away on holiday and will make his mind up when he returns next week.
"If Jimmy decides he wants to go to Celtic then we won't stand in his way. He has to consider what he wants to do".
Celtic last week