United were reduced to 10 men in Thursday's 2-2 Europa League draw with Sevilla when defender Martinez was carried off injured, after fellow centre-back Varane had to be replaced due to injury at halftime.
Asked for an injury update, Ten Hag said he didn't have one, telling reporters: "It's not even 24 hours. I don't have a complete diagnosis so I can't tell at this moment.
"I have an idea (about what it is) but I don't want to fuel speculation," the Dutch manager added, speaking ahead of Sunday's trip to Nottingham Forest.
"I have a lot of faith (in Lindelof and Maguire). We still have decent centre-halves. They've proved in the past and they've proved this season. We have four or five very good centre-halves who can do the job."
United are also short-staffed up front, with top-scorer Marcus Rashford ruled out of action for "a few games", while winger Alejandro Garnacho has been sidelined by an ankle injury, leaving Anthony Martial as their main attacking outlet.
The Frenchman started the midweek game against Sevilla, but Ten Hag said it could be too risky to include the injury-prone forward in the starting line-up for the game against Forest.
"We don't have so many options in the frontline with Rashford and Garnacho injured, so we have to be careful," Ten Hag said.
"We know if we put on a lot of load he gets injured, so we know we have to build it slowly and, when recovery time is less (between games), we have to manage it and be careful."
Ten Hag added that left-back Luke Shaw and midfielder Scott McTominay could return to the squad for Sunday's game, providing United a boost in their bid to seal a spot in next season's Champions League.
United are fourth in the standings, three points ahead of fifth-placed Tottenham Hotspur, who have played one more game.
"Every game is a battle, every game is a fight and you have to be ready for that fight," Ten Hag said.
"We have a squad. I have said all season we have more than 11 starters. When the time is there you have to show and contribute to the team and you have to be ready."
