Snodgrass left the London Stadium to join the Baggies on an 18-month deal earlier this month.
He then enjoyed an impressive debut with the former Scotland international playing an influential role in the derby victory over Wolves.
Albion boss Sam Allardyce was eager to add the 33-year-old to his ranks both for his quality and the leadership and experience he brings to the dressing room.
But while Snodgrass had been made available for transfer by West Ham - they did not want him playing against them tonight.
The Express & Star understands the Hammers initially told Albion they wouldn’t sanction Snodgrass’ transfer until tomorrow (January 20).
But the Baggies wanted him to play against Wolves and get to know his new teams mates as soon as possible.
And that led to the two clubs coming to an agreement preventing the midfielder from playing tonight, but he will be available to face his former club when the two sides meet again in May.
The Express & Star understands Albion could have signed Snodgrass last summer - a transfer that would have allowed him to play in both fixtures against the Hammers. But former boss Slaven Bilic opted to sign Filip Krovinovic on loan instead.
When in charge of West Ham, Bilic sanctioned a loan move that saw Snodgrass join Villa.