The BBC and Sky Sports television quoted the team doctor as saying the 25-year-old had suffered a 'trauma in his ankle' during training in north London.
"At the moment it is too early to say anything about him," said doctor Rodrigo Lasmar.
"On Friday, we watch to see what happens and then decide if we need to do any exams or not."
Sky reported he had been caught on the ankle by team mate Casemiro. Video footage showed the player hobbling after the tackle.
Manchester United this week agreed to sign Fred from Ukraine's Shakhtar Donetsk in a deal that British media have put at some 52 million pounds.
Five times World Cup winners Brazil have been using Tottenham Hotspur's training ground to prepare for the tournament. They play a friendly against Austria in Vienna on Sunday.
(Reporting by Alan Baldwin, editing by Toby Davis)
