The England international has been a regular in Jose Mourinho’s first-team so far this season despite the impressive form of Anthony Martial.
Rashford dropped to the bench for Manchester United’s 4-2 victory at Watford before he was a substitute in the Red Devils’ 3-1 win at title rivals Arsenal.
His compatriot Jesse Lingard seized his chance to impress the Manchester United manager with three goals in their two games in the English capital.
Rashford made his mark in the Champions League on Tuesday night with Manchester United’s second goal in a 2-1 win over CSKA Moscow at Old Trafford.
The 20-year-old has scored eight goals and has made four assists in all competitions so far this season.
However, former Manchester United midfielder Scholes wants Rashford to show more composure in front of goal to become a top Red Devils player.
“He’s still very young. He’s got the ability to beat people and has got fantastic movement,” Scholes told BT Sport.
“He just needs to add that little bit of composure and calm himself down in front of goal. I think he’ll be a top player for Man United.”
Rashford made his Manchester United debut in the Europa League under Louis van Gaal in 2015.
The Red Devils striker scored eight times in 18 games in all competitions in the 2015-16 season.
Manchester United finished in sixth place in the Premier League last term but won the Europa League and the League Cup.
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