Manchester United open their Premier League campaign against the Blues for the first time since the 2004/05 season when they lost 1-0 at Stamford Bridge.
If United are to avoid drawing a blank again, Rashford will be integral, especially in the wake of Romelu Lukaku’s £73million move to Inter Milan.
The 21-year-old often led the line under Solskjaer last season and is expected to resume that responsibility this campaign.
And former striker Nicholas believes the England international can be the difference when United face Frank Lampard’s side at Old Trafford.
“Solskjaer wants the crowd to believe they are better,” the pundit told Sky Sports.
“I don’t think United are, so I am going to go for a low-scoring affair.
“I am looking for Marcus Rashford to be a proper number nine and I see him being the match-winner on the day.”
United focused on their defence in the recent transfer window, signing Harry Maguire and Aaron Wan-Bissaka for a combined £130m, as well as £18m winger Daniel James from Swansea.
Nicholas reckons there will be more outgoings at Old Trafford before the European deadline strikes on September 2, though.
“Ole Gunnar Solskjaer is trying to get certain players out and certain players in. We will know the formation and style by Sunday,” the Scot added.
“Romelu Lukaku is [gone] and he will have to sell Paul Pogba and Alexis Sanchez too – he has another three weeks or so to do that.”
As for Chelsea, Nicholas is expecting a more inexperienced side than usual.
“Chelsea are under the transfer embargo and so the youngsters will come in. They will have issues defensively [after losing David Luiz],” Nicholas said.
“Chelsea will want to go to Old Trafford and walk away with something, with Frank Lampard getting through his first assignment without a defeat to his name.”