McTominay is back quicker than expected from a groin operation and is thought to be in contention to make a timely return to the Man United midfield against the Hammers.
Marcus Rashford has returned to training following a shoulder injury, but this match will come too soon for the attacker, while Amad Diallo and Edinson Cavani are still unavailable for selection.
Paul Pogba would likely be moved to the left if McTominay can prove his fitness, meaning that Jadon Sancho, who has struggled to perform in the early stages of the season, would drop to the bench.
Mason Greenwood, Bruno Fernandes and Cristiano Ronaldo are certain starters in the final third of the field, while there are also unlikely to be any surprises at the back.
Dean Henderson is now available after recovering from coronavirus, but David de Gea has been in strong form this season, while Aaron Wan-Bissaka - sent off in Tuesday's 2-1 loss to Young Boys in the Champions League - should hold off competition from Diogo Dalot to start at right-back.
Nemanja Matic is also an option in midfield and could start if McTominay does not make it, with Solskjaer set to name two defensive midfielders in a 4-2-3-1 formation at the London Stadium.
Manchester United possible starting lineup: De Gea; Wan-Bissaka, Varane, Maguire, Shaw; McTominay, Fred; Greenwood, Fernandes, Pogba; Ronaldo