The Slovenian drew the ire of Mourinho during the Portuguese's second spell in charge of Chelsea after failing to award a penalty during a 0-0 UEFA Champions League group-stage draw at Dynamo Kiev last season.
"The referee was weak and naive. Big penalty," Mourinho said at the time, although it mattered little in the long run as Chelsea went on to qualify as winners of their group.
United booked their place in the Europa League showpiece in Stockholm later this month with a nervy 1-1 draw at home to Celta Vigo, which secured a 2-1 aggregate success.
Skomina, an international referee since 2003, has presided over six Champions League matches this season, including Monaco and Borussia Dortmund's quarter-final, second leg.
Meanwhile, 41-year-old German Felix Brych has been given the task of officiating the Champions League final between Real Madrid and Juventus in Cardiff on June 3.