O'Donnell is out of contract himself at the Bescot Stadium and has failed to agree terms with Walsall over a new deal.
The Chronicle understands that boss Steve Clarke has identified the League One stopper, who kept 21 clean sheets in 54 games this season, as the potential replacement for Federici.
The 26-year-old is highly thought of at Walsall and manager Dean Smith is hopeful that the keeper will choose to stay at the Bescot Stadium.
But talks have stalled and O'Donnell is keen to explore other options for next season, with plenty of suitors from the Championship interested in the highly-rated keeper.
Reading are one of the interested parties and Clarke could move to lure O'Donnell to the Madejski Stadium as next season's number one, if a contract can't be agreed with Federici.
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