The England international started all three of their Premier League games in October, helping Manchester United to collect seven points and hoist themselves up the table.
Rashford had an important role as the Red Devils to come from behind to secure a 3-2 win over Newcastle United before the international break, before the striker played 85 minutes of their 2-2 draw at Chelsea FC last month.
Mourinho made the decision to drop Romelu Lukaku and start Rashford in a centre-forward role rather than on the wing for the visit of Everton at Old Trafford last weekend.
Rashford produced a solid performance in the striker role before Lukaku replaced the Englishman in the 65th minute of the 2-0 win over Everton.
Rashford has scored one goal and has made one assist in his last 10 games in all competitions for Manchester United ahead of their trip to Bournemouth on Saturday lunchtime, suggesting the striker is lacking confidence.
However, Shearer, who is the Premier League’s record goal-scorer, believes Rashford needs a run of games in a centre-forward role to build his confidence.
“He did not exactly sparkle against Everton, managing only one shot at goal in his 65 minutes on the pitch, but I still think Marcus Rashford deserves to keep his place leading Manchester United’s attack,” Shearer told BBC Sport.
“I would love to see that happen. Rashford has clearly got huge ability and has a big future for club and country, but his situation at United at the moment is a tough one for a young player to flourish in.
“As his manager Jose Mourinho points out, Rashford is playing regularly and getting minutes on the pitch – but usually that is as a right or left-sided forward.
“When he gets a chance ahead of Romelu Lukaku at centre-forward, as he did on Sunday, he is under huge pressure to make that chance count because he is keeping a £75m striker out of the team.”
Rashford was a revelation when he burst onto the scene at the Theatre of Dreams during Louis van Gaal’s final season in charge of the 20-time English champions.
The 21-year-old netted eight times in 18 games in the 2015-16 season after he found the net twice in a 3-2 win over Arsenal in his Premier League debut.
Rashford has featured in a lot of games since Mourinho took over the reins from Van Gaal in May 2016, although a good portion of those appearances have been from the bench.
And Shearer admitted that Rashford has found it difficult to thrive at Old Trafford in recent seasons.
He added: “It has been a difficult environment for Rashford, yet he is still expected to make an immediate impact whenever he comes in at centre-forward – otherwise people will always question whether he should be starting in that position.
“It is not surprising that he seems to play with more freedom when he is in an England shirt because, certainly for the last three or four months, international football has probably been more enjoyable for him.”
Rashford has netted 25 times in 125 games under Mourinho to average a goal every five games since the Portuguese head coach became the third manager of the post-Sir Alex Ferguson era.
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