United's shock Champions League victory at Paris Saint-Germain last week carried them through to the last eight and all but confirmed Solskjaer will soon be named Jose Mourinho's successor on a long-term basis.
Since that famous evening in France, United have tasted defeat for the first time in England on the interim manager's watch, beaten 2-0 in last weekend's league visit to Arsenal.
But although that setback dented United's bid for a top-four finish, it did little damage to Solskjaer's standing, especially given the nightmare injury list he has endured recently.
Some reports have suggested Solskjaer could be confirmed as manager during the forthcoming international break, which follows the Wolves Cup tie.
United officials have offered no guidance on whether the appointment is imminent, but it emerged last week that Solskjaer does not, as was commonly thought, have a contract with his former club Molde.
He revealed that, with regulations forbidding a manager from having concurrent contracts with more than one club, he tore up his deal with the Norwegian side to join United in December.
It is understood United and Molde have put in place a compensation package should Solskjaer win the post permanently, with a figure of around £500,000 ($665,000) mooted.
However, the United hierarchy, led by executive vice chairman Ed Woodward, have another burning personnel issue to resolve as the club seek to appoint a director of football.