Manchester United failed in a late attempt to sign Kieran Trippier, according to reports.
Solskjaer is a fan of Trippier's versatility which has allowed the 30-year-old to play at right-back, left-back and as a wing-back throughout his career.
United finally made their move on deadline day but were unable to agree a deal with Atletico before the deadline at 11pm BST.
Sport1 reports that the Red Devils submitted an £18m bid for Trippier on Tuesday.
The England international was keen on a return to the Premier League after two years in Spain.
He also favoured a move to United over Arsenal, who were also linked with his signature before they acquired Takehiro Tomiyasu from Bologna.
Had Trippier completed a switch to Old Trafford, it would have seen Diogo Dalot join Borussia Dortmund on loan.
But United's failure to land the Englishman means Dalot is staying put to serve as deputy to Wan-Bissaka.
United's offer of £18m was deemed insufficient by Atletico, who view Trippier as an integral part of their team.
The former Tottenham man won the La Liga title at the Estadio Wanda Metropolitano last season.
He has another two years on his contract with Atletico, who will hope to win a second successive championship this term.
United will be disappointed to have missed out on Trippier, but a transfer window that has brought the arrival of Cristiano Ronaldo, Jadon Sancho and Raphael Varane can only be seen as a positive.
The pressure on Solskjaer could soon ramp up, though, with United now possessing one of the most talented squads in Europe.
The Norwegian has yet to win a trophy as United manager and a failure to do so this season could spell the end of his employment in Manchester.
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