The 22-year-old was only snapped up by the Bees last summer, with Premier League interest fended off as they secured his services from Leyton Orient on a three-year contract.
Just 12 months into that agreement and his future is being called into question once again.
Odubajo is of interest to Hull having proved himself to be a more than capable Championship performer in 2014/15, being a virtual ever-present for Brentford as they made the play-offs.
The Tigers are hoping to be in the promotion mix this season, as they seek an immediate return to the Premier League.
Steve Bruce has already been heavily linked with a raid on Brentford for Andre Gray, with the Hull Daily Mail reporting on a failed bid.
It may be that he enjoys better luck in his pursuit of Odubajo – a versatile performer who can operate at right-back or on the wing – with a formal offer now on the table.