The Argentina international is struggling with a minor injury after he was replaced with 17 minutes to go in their 2-1 defeat by Arsenal in the FA Cup quarter-final on Monday night.
United manager Van Gaal, whose side are fourth in the Premier League table, confirmed that the £16m summer signing could miss the clash against top-four chasing Spurs.
“Rojo is a little bit injured. You have to take care of the health of the players. He has a minor problem. Maybe I’ll take him out of the game against Tottenham Hotspur, but I have to decide,” Van Gaal told MUTV.
United full-back Luke Shaw was replaced by Phil Jones in the second half of their FA Cup defeat, but the England international is fit for the visit of Tottenham.
Meanwhile, 31-year-old Dutch striker Robin van Persie is still sidelined with a hamstring problem that he picked up in a 2-1 defeat by Swansea City last month.
“More or less, only van Persie is injured. That is a good sign – when you have a defeat and all your players want to train and show the energy in the training session. That’s good to see,” Van Gaal added.
United are three points ahead of sixth-placed Tottenham.
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