The 21-year-old was one of the most highly-rated young players in the Europe when he signed for United in a £19 million deal from FC Porto in 2018, but he has had to be patient having made just 33 appearances in his two years at the club.
Ashley Young was providing back up before moving to Inter Milan in January. Solskjaer is open to adding another defender to his squad in the next transfer window but the search is likely to focus on a centre-back.
Injury has restricted Dalot to four Premier League appearances this season but he should be available for the final weeks of the season if the campaign gets the green light to resume in June.
Solskjaer's squad returned to training on Wednesday while observing social distancing measures.
Meanwhile, United defender Max Taylor has signed a new deal.
The 20-year-old, who was diagnosed with testicular cancer in 2018 but has since returned to training and was included in the squad for the Europa League tie against FC Astana in November, has agreed a one-year extension.