While a certain amount of priority is being placed on ensuring that either Romelu Lukaku or a direct replacement is available at the end of play on Thursday, Solskjaer remains eager to bring in a new midfielder.
Sporting Lisbon's Bruno Fernandes is still being linked with a transfer to Old Trafford, but Tottenham Hotspur playmaker Christian Eriksen is seemingly considered to be the most likely addition.
Spurs do not want to risk losing one of their most prized assets on a free transfer at the end of the season, leaving United to negotiate a deal for the Denmark international.
However, there would be question marks over where Eriksen would feature in Solskjaer's team, partly due to Paul Pogba remaining with the Premier League club.
Here, Sports Mole predicts how the creator could be used by the Norwegian for the upcoming campaign.
While having Eriksen and Pogba at his disposal would be deemed to be a positive, it also has the potential to create problems for Solskjaer, who will want to ensure that his side improve on their poor defensive record last season.
Much like the World Cup winner, Eriksen is capable of playing as the most advanced of a midfield three, or in a role closer to the main striker.
However, should Eriksen and Pogba be included in the same starting lineup, they will likely be deployed either side of one of those pair, potentially McTominay due to his greater mobility.