The striker posted a picture of Solskjaer telling him, Jesse Lingard and Anthony Martial a story during United's warm-weather training break in Dubai.
He captioned it: "'Seconds left.. Becks whipped in a perfect corner. Teddy flicked it on. The rest is history' ? @ManUtd"
Rashford's reference to Solskjaer's winning goal in the 1999 Champions League final against Bayern Munich only added to the feel-good factor at Old Trafford.
United supporters, jubilant after five wins out of five since the Norwegian's arrival, went into meltdown over the post.
Fan group Devils of United tweeted: "What a f***ing tweet. 10/10. United through and through, love it."
Another added: "Might be the best tweet ever written."
One user wrote: "An early runner for tweet of the year."
The photo is evidence of Solskjaer's excellent man-management skills, which Lingard says are getting the best out of the players.
Lingard said: "Ole’s great one-on-one with players.
"It’s great man-management. He will always speak to you and tell you what to do.
"He knows what kind of a player I am. When I am on the right wing he likes me to come inside and make things happen.
"He gives me licence and freedom to do that. He’s very special. He knows where Man United has to be and that is at the very top."
The gloom around Old Trafford has lifted since Solskjaer replaced Jose Mourinho in December.
Solskjaer, 45, became the first top-flight manager since the football league was created in 1888 to have won their opening five games by at least a two-goal margin after Saturday's 2-0 FA Cup win over Reading.
Fans and players alike are calling for him to be given the job on a permanent basis.
Interim boss Solskjaer returns to Molde at the end of the season but admits he would love to stay.
Speaking after last week's 2-0 win over Newcastle he said: "I don’t want to [leave] – of course I don’t.
"It’s such a great bunch of players, fantastic atmosphere, but it’s the next game, it’s the next game.
"I’m doing my job as long as I’m here. If you win four you can win another four with this club.
"That’s the challenge, that’s the standard we know. That used to be the challenge from the gaffer [Sir Alex Ferguson]."
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