Kilmarnock are said to be ready to cash in on the one-time Celtic youth team player.
O'Donnell, who has seven caps for Scotland, is about to enter the final year of his contract.
But despite being offered a new contract, nothing has been signed so far - prompting English Championship clubs, and potentially Celtic, to monitor his situation, the newspaper claims.
Celtic are seemingly set to lose a trio of right-backs, Jeremy Toljan, Mikael Lustig and Cristian Gamboa, at the end of their deals this summer.
And that makes O'Donnell a logical target for Celtic - especially having been part of the youth system during Lennon's first spell in charge of the Bhoys.
The 27-year-old left for Partick Thistle in 2011 and moved to Luton Town before making a return to Scottish football with Kilmarnock two years ago.
Would the Kilmarnock man be a good addition for Celtic?
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