Odubajo was brought to Hull City by Aston Villa boss Steve Bruce.
Consequently, Odubajo - who was brought to Hull by Villa boss Steve Bruce - will leave the KCOM Stadium for free this summer.
The versatile right-back has already been linked with a move to Villa Park this summer, courtesy of the Hull Daily Mail.
Although it remains to be seen whether Aston Villa will pursue Odubajo's signature, after tying Alan Hutton to a new deal on Thursday.
However, given their current financial state, it would still make sense for Villa to do a deal for Odubajo if they can find buyers for others in his position, for example James Bree and/or Ritchie de Laet.
The only downside to signing Odubajo would be his recent injury record.
The former England Under-21 international has missed the whole of the past two seasons with knee ligament damage.