Both Premiership clubs have been linked with O'Dea this year and his agent, Kevin Moran, said: "Darren is extremely frustrated at the moment and you can count on one hand the number of games he has played for the first team over the past year.
"We will be asking again at Christmas if he can go out on loan. There were options for him in the Coca-Cola Championship in August but Celtic would not allow him to leave Parkhead.
"He's desperate to play first-team football in order to develop. He has been in the full Republic of Ireland squad for Giovanni Trapattoni but that's unlikely to happen again if he's sitting on the sidelines or playing reserve games.
"It is very hard when you have come in against AC Milan and done well. You want to kick your career on from that rather than find it going backwards. We will see what happens in January."