The centre-back has endured a difficult season in Italy following his £67.5million move from Ajax last summer.
United were among the clubs vying for his signature, along with Barcelona, before being forced to admit defeat when he set his heart on Juve.
But they have continued to track his situation in Turin, with Solskjaer still a firm admirer of the 20-year-old.
And despite United’s manager focusing on his attack this summer, he is still to find an ideal partner for Harry Maguire in the heart of defence.
De Ligt has struggled to emulate his outstanding form for Ajax, which saw him play a key role in the Dutch giants’ charge to the Champions League semi-final last season.
His future has been the subject of constant speculation, with growing suggestions he will be allowed to leave in the summer.
Solskjaer still considers De Ligt among the best central defenders in the world.
United have been long-term suitors, but opted against a move two years ago over concerns that he could be susceptible to weight gain.
Their ongoing interest also raises the possibility of a part-exchange deal being struck over Paul Pogba.
Juve are among the clubs hoping to lure the France international away from Old Trafford this summer – but United have severe doubts that anyone will meet their £150m valuation.
Using De Ligt as a make-weight would go a long way to offsetting that cost.
Solskjaer has been promised the funds to complete his rebuild this summer, with Jadon Sancho his top target.
Jack Grealish and James Maddison are also on his wish list, along with a centre forward.