Odubeko joined on a season-long loan in August, but a lack of time on the field has seen the 19-year-old return to east London.
The Irish striker made just six substitute appearances, all from the bench. Four were in September and only two for more than 15 minutes. His final (and longest) appearance came as a 55th-minute substitute at Barnsley in early December.
Coach Carlos Corberan has always spoken well of the youngster but Danny Ward has proven much more durable this season, appearing in 23 of 26 Championship matches this season, and scoring seven times.
Fraizer Campbell has also struggled for game-time as a result.
He has been restricted to just four Championship starts this season, and is yet to score.
Summer signing Jordan Rhodes has recovered from the back injury which kept him out for more than two months.
At Blackburn Rovers on Sunday, when Ward was ill (not with coronavirus), the Terriers played Josh Koroma at the head of the attack, with Rhodes coming off the bench.
It may be, therefore, that Town do not look to bring in a replacement for Odubeko.
With Pipa also making his comeback after injury over Christmas and Jonathan Hogg expected to return soon, they are in good shape, and have loaned 20-year-old Josh Austerfield and 18-year-old Brahima Diarra to League Two Harrogate. Both made debuts at against Carlisle United in the Football League Trophy last night.
Having not played for West Ham this season, Odubeko is free to go back out on loan to another club, perhaps lower down the pyramid.
Barnsley left-back Ben Williams is expected to make a permanent move to League One Cheltenham Town.
The 22-year-old left-back has been restricted to just five appearances this season, the last against Millwall on October 2. He has not featured in a matchday squad since Poya Asbaghi took over as coach in late November.
Barnsley have already released forward Dominik Frieser ahead of what is expected to be a frugal January for the Oakwell club, despite the looming threat of relegation to League One.
The Reds are just three points above bottom-placed Derby County, who had 21 deducted for financial issues.