Pogba reprised his stuttering spot-kick run-up and Solskjaer said: "He has scored quite a few goals hasn't he, so if he's comfortable with it, as long as the ball goes in the net..."
However, the Manchester Evening News say Solskjaer almost did not land the role.
Rashford, 21, made his 150th Manchester United appearance in the 2-1 win over Brighton on Sunday, reaching the mark at a younger age than both Rooney and Ronaldo.
Rashford marked his 150th club game with a fine goal against Brighton, finding the top corner from an acute angle.
After Gross pulled a goal back in the 72nd minute, it was a nervy conclusion for the hosts but they managed to see out the victory as Solskjaer became the first United boss to win his first six league games. He will stand up for a fight and stand up for himself and a teammate.
"Definitely, he can be absolutely top-class", Solskjaer told reporters when the comparisons were suggested to him.
"We were under the cosh, we were winning 2-1, so keep it away from the opposition, let them run". "I haven't spoken to him many times".
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Chris Hughton's south coast side are seven points clear of the relegation zone, and face Fulham, Watford and Burnley in their next three league fixtures, following next weekend's FA Cup fourth-round tie against West Brom.
Rashford saw his influence fade as United exhausted, and it proved to be a nervous finish after Gross pulled a goal back with 18 minutes left.
Manchester United are now a different side since the last time they played Brighton.
'When I think of United from years ago with [Cristiano] Ronaldo, [Wayne] Rooney, [Carlos] Tevez, all three of them would pop up in different areas of the pitch.
Solskjaer has proved he has the temperament for the role, calmly describing Mourinho as a "fantastic manager" when asked about the pronouncements his predecessor has been making as a television pundit in Doha.
However, Southgate stated that the most important thing concerning Rashford is not where he is being deployed by his club but that he is getting regular first-team minutes. "They're probably pressing higher, and they've got a really good momentum at the moment".