Hull have confirmed they've made an offer for Fortune, who spent last season on-loan at West Brom.
And new Celtic No2 Peter Grant admitted: "Marc says he would love to come here and he is a player we'd be very interested in if he was available and affordable.
"Marco is a quality player and we were very impressed by just how well he did for us last season.
"People say he didn't have a fantastic scoring record. But look at the goals from midfield after he came in.
"The goals the other boys scored because of the way he played was phenomenal.
"Marco had a great ethic about him in his training as well as his playing. He was a privilege to work with."