Courtois did not feature for Belgium during the international break because of a hamstring problem, while defender Christensen was sent back by Denmark after struggling with muscle fatigue.
Both are serious doubts for Sunday’s match at Stamford Bridge, where a defeat could prove fatal to Chelsea’s hopes of qualifying for the Champions League.
“We have two big problems — Courtois and Christensen — and we have to check the real possibility to play, and then to play well,” said Conte on Thursday.
“The most important thing is to be available but, at the same time, to have the right physical condition to play a good game. Otherwise I have to make a different decision.
“At this moment for me it’s very difficult to tell you with accuracy which is my choice for Sunday because we have to check these two situations.”
Should Courtois fail to be fit, new Argentina international Willy Caballero would be his obvious replacement, while Gary Cahill could come in for Christensen.
Centre-back Cahill has fallen down the pecking order under Conte this season and was left out of Gareth Southgate’s latest England squad.
He looks to be the only other option available to his club manager, with David Luiz ruled out with a knee injury.
“David Luiz is out at least for another three weeks. He’s recovering from a problem in his knee,” said Conte.
Conte’s champions are playing catch-up in the race for a top-four finish but victory this weekend would cut the gap to fourth-placed Spurs to two points with seven matches to play.
While Courtois and Christensen may yet be available against Mauricio Pochettino’s men, midfielder Ross Barkley will definitely be absent.
The January signing is scheduled to play in a reserve game this weekend in his attempts to return to full fitness.
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