Celtic had been in talks to sign the Londoner, Bhoys boss Brendan Rodgers admitted last month.
Odubajo left Hull at the end of last month and had been in talks to join Celtic, Bhoys boss Brendan Rodgers admitted last week via the Daily Record.
The 24-year-old has not played competitively for more than two years, however, and is likely to have to prove his fitness before another club agrees to take him on.
Although many of a Brentford persuasion, who watched Odubajo for a season earlier in his career, appear to be keen on a deal regardless.
This is what they are saying on Twitter...
Sign him up— Alfie Chapman (@alfiebfc99) 3 July 2018
what are you doing to me! Imagine......— Stuart Wakeford (@StuSoccerAm) 3 July 2018
Just sign the guy— Craigo (@craigBFCtillyer) 3 July 2018
Hunt over.... sign him up— Thebfcbeesblog (@thebfcbeesblog) 3 July 2018
Bring him home lads— Joe S (@Joe_bees19) 3 July 2018
If you sign him I promise I will reconsider my decision not to renew my season ticket. I will even buy one of the hideous brown and orange shirts.— Jimmy (@JimboUpNorth) 3 July 2018
Please sign— George (@GeorgeL014) 3 July 2018
I want to see him sign by the end of the week lads! get it done— Owen Crote (@owencrote) 3 July 2018
quality player needs to get his carear back on track and theres no better place to do it then with the mighty bees— Jake (@jakeforsdyke19) 3 July 2018
Football and Odubajo are coming home https://t.co/W3mFQrMBae— Jordan Nugara (@JNugaraBFC) 3 July 2018
It remains to be seen whether Celtic have officially ended their interest in Odubajo, although that would appear to be the most likely outcome, following Tuesday's development.
And with Mikael Lustig, Cristian Gamboa and Anthony Ralston on board, that should not come as too much of a blow to thw Bhoys.
Londoner Odubajo helped Brentford to the Championship play-offs in his solitary campaign at Griffin Park, before being sold to Hull City for £3.5 million - around three-and-a-half times what the Bees are reported to have paid initially.
Are Celtic missing a trick if they pass up on Odubajo?