Caretaker manager Solskjaer has won his opening five matches after replacing Jose Mourinho last month – equalling Busby's record from the 1946-47 season in the 2-0 FA Cup victory against Reading.
Solskjaer could surpass Busby's feat with victory against high-flying Tottenham at Wembley on Sunday but the United favourite is not interested in the landmark.
"I don't care," Solskjaer said. "Not now. I might sit down in 20 years' time and look at whatever records I have.
"When I'm in a position, I never look back on what I'm doing that way. Never, ever."
United's four successive Premier League victories have seen the Red Devils move within three points of fifth-placed Arsenal, having scored 14 goals and conceded just three.
Tottenham are 10 points better off than United in third position, with Spurs manager Mauricio Pochettino reportedly the favourite to succeed Mourinho at the end of the season.
"Spurs away, that's a proper test," Solskjaer said. "They have performed fantastically this season, they've got a great way of playing. There will be loads of things we need to look at.
"He [Pochettino] has got them performing really well over the last few seasons. Both as individuals and we have to look at the team unit and how we play against them."
On United's quest to qualify for the Champions League, Solskjaer added: "I'm not going to say top four is our target because my target is also a certain way of playing. That certain way of playing will get us to where we belong in the end. It depends on the performances."