Celtic have since strengthened in O'Donnell's position.
But the Kilmarnock and Scotland player has claimed that no clubs came in for him in the most recent transfer window - and he is not expect anything different in January despite being in the final year of his contract.
In quotes published by The Daily Record on Tuesday, O'Donnell confirmed that he has been offered an extension by Celtic's Scottish Premiership rivals, but stressed that there has not been any progress made.
A decision, he explained, is likely to come towards the end of the season - provided he has not been sold by then.
"Look, no one came in for me in the summer, so I don't see why it will be any different and someone comes in for me in January," O'Donnell is quoted as saying.
"If it does happen then there is a different question to be asked and we'll need to look at it.
"But just now I'm happy, we're winning and while I don't think my personal performances have been great, hopefully there's more to come from myself and more to come from the rest of the team."
Celtic signed Moritz Bauer, Hatem Abd Elhamed and Jeremie Frimpong to play in O'Donnell's primary position in the summer transfer window - although Bauer's loan deal expires next summer.
O'Donnell, who was on Celtic's books as a youngster, recently signed up to the StormSportsX agency, to which the Bhoys players Jack Hendry, Jonny Hayes and Calvin Miller also belong.
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