Amad Diallo also has officially left on loan, joining Scottish side Rangers on Thursday through the end of the season. Amad, 19, made a total of nine first-team appearances at United, registering one goal and one assist, but has played for the club just once this season. Capped three times by Ivory Coast, he joined United in January last year from Serie A club Atalanta, where he made his professional debut.
Talks are ongoing with Palace about a loan for Van de Beek but there is also interest from clubs in Spain and Italy. United are keen to receive a loan fee before letting the Dutchman leave and will ask that his wages are covered as part of any deal.
Rangnick was initially reluctant to sanction so many exits halfway through the season but the performances of Elanga have convinced the German he would still have enough options to navigate games in the Premier League, FA Cup and Champions League.
The 19-year-old has started United's last three games and scored in the 3-1 win over Brentford.
Sources have told ESPN that loan interest in the Sweden Under-21 forward this month has been firmly dismissed.
Rangnick expects Elanga to play a number of games between now and the end of the season and will compete with Marcus Rashford, Jadon Sancho and Mason Greenwood for one of the wide positions in his 4-3-3 system.
Paul Pogba's return after more than two months out with a thigh injury will also boost Rangnick's squad. The Frenchman will be a free agent in the summer but will not leave this month.
The midfielder has been training in Dubai during the winter break and is in line to make his comeback against Middlesbrough in the FA Cup fourth round on Feb. 4. The squad are expected back in training at Carrington on Saturday to begin preparations for the game.