The Old Trafford giants are on course to have two players hit the 20-goal mark in the same campaign since since Dimitar Berbatov and Javier Hernandez in 2010-11.
Martial's maiden hat-trick took him level with Rashford on 19 goals, while 18-year-old academy graduate Greenwood has found the net 13 times in a superb breakthrough season.
The trio have stepped up after Solskjaer allowed Alexis Sanchez and Romelu Lukaku to depart for Inter Milan last summer, but the former striker's happiness comes with a hunger for them to kick on again.
"Romelu's a very good goalscorer – he'll score goals in any team that he plays in," the United boss said. "It was time now for him to move on and pursue other dreams.
"For us, as a group, it was time to allow our forwards to feel that confidence and feel that almost demand of playing and being demanded that you play every game, two, three, four games, five, six, seven games on the bounce and perform.
"Because in the end that's how you get to another level, a different level.
"I think all three that we have talked about have had a good development this season – but they can be so much better.
United are unbeaten in 14 in all competitions and have a chance of lifting a trophy this season, but they are an eye-watering 37 points behind Premier League champions Liverpool and lie sixth ahead of Tuesday's trip to Brighton.
"It's the Premier League, with quality players and quality teams, so I would never ever say 'this is an easy game' in the Premier League," he said when a potentially kind run-in was mentioned. "Absolutely no chance.
"We just have to focus on one game at a time, win this one so we can go into the next one feeling more confident.
"But also push on because complacency, that kicks you somewhere you don't want to get kicked in football, and any game is a difficult one."
Tuesday not only brings attention on the field but off it as highly-rated Angel Gomes' contract expires, with Solskjaer admitting it "doesn't look like" the teenager will be staying despite a contract offer being on the table.
"Well, you can ask Angel why he's not signed," Solskjaer said. "He's not signed yet, there's still... I don't know where, what the talks are behind the scenes.
"Angel's a top kid. Of course there's people around him that advises him to do different things.
"If he doesn't sign, all the best to Angel. I'm going to follow his career if he doesn't sign for us. If he signs for us, let's kick on."