Paul Pogba has all the attributes to be that individual, but whether the Frenchman remains at the club amid serious interest from Real Madrid, coupled with his own desire to leave, is uncertain.
Solskjaer also overlooked Pogba for the second half captaincy in United's opening pre-season friendly against Perth Glory on Saturday, instead handing the armband to Juan Mata.
"We need to win again," Solskjaer said, as quoted by The Telegraph after attending a fan event.
"I never had the honour of playing with Robbo but we need a player like him in the team. We're waiting for the young ones to come through because we've got so many exciting players and I'm sure we'll see the best of them in the years to come. There are some experienced ones as well that still have a few years left in them. We can get back to the level we were, definitely."
United are thought to be chasing young Newcastle midfielder Sean Longstaff, although the Magpies' reported resistance to selling for anything less than £50m could make that difficult.
There is also increased speculation that a firm offer for Sporting CP star Bruno Fernandes is imminent. The Independent reports that a £50m 'concrete bid' will be made for the Portugal international before the transfer window closes in three weeks.
In terms of existing players, there is optimism that David de Gea is set to finally end the uncertainty over his future and sign a new long-term contract with United.
De Gea is in the final year of his current deal, but there has been much talk in recent weeks about a £350,000-per-week offer and the Daily Telegraph claims the 28-year-old is now expected to put pen to paper and commit his future at Old Trafford.