The 24-year old Republic of Ireland international has a year remaining on his Celtic Park contract and has vowed to become a first team player under Neil Lennon.
O'Dea made it clear that he does not want another loan and even though he is determined to win his place back in the Celtic firs team, he and his agent will keep their eyes and ears open for any potential transfers that may arise.
"I've got a year left on my contract at Celtic and I'll just have to wait and see what happens in the summer," he said.
"Nothing really happens between now and pre-season, so my only aim is to do well with Ireland then look at it at the start of the season.
"Whether I'll be at Celtic, I don't know. I certainly will not be going out on loan again and we will just have to wait and see whether I go permanently or not.
"I really don't know what will happen. But I won't be going up to Scotland to warm the bench at Celtic.
"I've only a year left. Celtic have been fantastic to me and I owe my whole career to them. I have given everything for them so I hope if I am to leave it'll be a clean-cut move.
"Listen, I am not saying that I am done at Celtic. I will wait and see what happens in the summer. I will probably be back there for pre-season and, if I do well during pre-season, then who knows?
"I'm sure my agent will be looking around at different clubs and assessing my options."