The right-back has been on the sidelines since suffering a knee injury in pre-season, and he is desperate to make his first Premier League appearance for the club.
Odubajo is back training with the rest of the Tigers squad and says it should not be too long before he is pushing for a place in Mike Phelan's starting eleven.
"It's a huge boost to be going back outside to work every morning. I feel like a footballer again, even though I'm not back to the playing stage yet," he told the club's official website.
"We have a fantastic medical team here and it feels like a blessing to be back to the stage I'm at now. I'm progressing really well and I think I've got about another month to go.
"Hopefully by the next international break I'll be in and around things, which is good. I went to see the surgeon last week and he gave the all-clear to get back outside with no real restrictions.
"It's a case now of trying to get back to where I was before in terms of fitness and taking it from there."