According to multiple sources, including The Telegraph, the Belgium international was not part of the squad that departed for Russia on Monday afternoon. He sustained a painful blow to his left ankle following a late challenge from Southampton striker Shane Long during a 1-0 Premier League win at the weekend.
There were 37 minutes on the clock at St Mary's when Long was cautioned by referee Craig Pawson for appearing to tread on Fellaini's Achilles' in a tackle that is said to have enraged United, who evidently feel that the Irishman should have been sent off.
Although he returned to play the full 90 minutes after receiving treatment on the pitch, the effects have clearly lingered with the 29-year-old and he has stayed in Manchester as his teammates departed for Moscow.
Further clarity on the situation and a potential time frame for his return is expected on Tuesday, when manager Jose Mourinho is due to face the media in his customary pre-match press conference.
United are already missing their most influential midfielder in Paul Pogba, who limped out of the first half of a 3-0 victory over FC Basel earlier this month with a hamstring issue. The Frenchman has already missed matches against Everton, Burton Albion and Southampton, with Mourinho still unsure as to exactly how long he will be out.
Sakari Orava, the respected Finnish surgeon who recently operated on Barcelona's Ousmane Dembele, said yesterday that a decision on whether or not Pogba is to go under the knife will be made this week.
"His injury is a little different to Dembele because he can heal without surgery," he said.
Nemanja Matic has travelled to Moscow in a boost to Mourinho's increasingly depleted midfield options, although it remains to be seen if he will be subject to a limited role after also sustaining a knock at Southampton. Long-term absentees Marcos Rojo and Zlatan Ibrahimovic (both knee) are not expected to return to action until after Christmas.
Eric Bailly is now eligible for European duty after being handed a three-match ban by Uefa following his late red card in last season's Europa League semi-final second-leg clash with Celta Vigo. He was subsequently sidelined for the final against Ajax and missed the Uefa Super Cup loss to Real Madrid in addition to that aforementioned defeat of Swiss champions Basel at Old Trafford.