Snodgrass has been in eye-catching form on a loan spell at Aston Villa, where he has notched six goals and claimed five assists in 21 Championship matches.
The Scot has struggled at West Ham previously, but Moyes wanted to give his fellow countryman a chance.
However, West Ham’s attempts to recall the 30-year-old have not worked out, due to terms in his deal with Villa.
The claret and blues have protected themselves from losing Snodgrass by paying a fee for the winger, and West Ham have no option but to leave him with Steve Bruce’s side until the end of the season.
If Snodgrass had returned it would have been a controversial decision, as the wide-man is not the most popular player at West Ham, due to his poor performances last season.
Moyes has suggested this week that he wants a right-sided player added to his squad, as he needs to cover for the injured Michail Antonio.
Even without Snodgrass, West Ham have been in good form of late and won their most recent outing 4-1 against Huddersfield Town.