Odubajo suffered a serious injury during the 2016 Premier League play-off in which Hull City defeated Sheffield United to win the golden ticket.
While his team-mates, including Shaun Maloney and David Marshall enjoyed a season in the top flight Odubajo was fighting a knee injury that was to rule him out of football for two full seasons.
In August the 25-year-old signed a one year contract with Brentford who had sold him on to Hull in 2015 for £3.5m.
Odubajo has now started five Championship matches for Brentford and made his fourth substitute appearance on Monday night in the 1-1 draw with West Brom.
Brendan Rodgers is expected to bring in a right-back during the January transfer window but despite his recent appearances it’s unlikely that the Irishman will make a move for Odubajo due to Celtic’s extensive fixture demands.