Hull are looking for a new manager, following the sacking of Phil Brown on Monday.
“I thought about leaving in January but I saw the supporters and said, ‘No I can’t do it’,” Grant said.
“I stayed, I’m fighting for the club and do not have any intention to give up. This club has become very important to me.
“I’d ask the new owner for some stability and I’m waiting for the day this club gets some stability.”