The 24-year-old has scored 12 goals in all competitions in an injury-hit season but has just one in the last six matches as United struggle for goals in the absence of striker Marcus Rashford, who is nursing a stress fracture in his back.
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"He's giving us everything. He's been asked to play -- he has started the last eight games -- and running probably 20% more than he did when I came here," Solskjaer told reporters.
"We'll give him more support, give him rest when he deserves it ... he's been asked to play too much as well, especially now when Marcus is injured.
"I know he's tired, but he's never ever dodged a training session. He's training, he's available for every game, so I'm delighted with the boy."
Rashford scored 19 goals in all competitions before injury struck while academy graduate Mason Greenwood has chipped in with 10.
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The club also signed 30-year-old Nigerian Odion Ighalo on loan from China's Shanghai Shenhua on transfer deadline day.
United, seventh in the Premier League with 35 points from 25 matches, visit Chelsea on Feb. 17.
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