Nagelsmann, whose sacking in March 2023 led to Tuchel's arrival, was tipped to return to Bayern, but has now extended his contract with Germany until 2026
The 32-year-old, who came through the youth ranks at Barcelona and won six La Liga titles, tore his cruciate knee ligaments in March and is without a club after leaving the Nou Camp at the end of last season.
"Valdes will have his recovery supervised by the United medical staff before training with the first team as he bids to regain full fitness," United said on their website (www.manutd.com)
Sixth-placed United host Premier League leaders Chelsea at Old Trafford on Sunday.