Manager Jose Mourinho told a news conference that the centre half missed a training session on Friday because of the ankle injury he suffered in the midweek 4-0 Champions League victory at Maccabi Tel Aviv.
The 34-year-old Terry is expected to undergo a fitness test before the game at White Hart Lane, a match that could prove pivotal in Chelsea's difficult season.
"I don't want to say that it's impossible he plays because maybe he plays and then you will say that I was hiding," said Mourinho.
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"I'm not hiding. Today he didn't train but we have a little hope that it's possible."
Mourinho offered a vote of confidence in the central defensive pairing of Gary Cahill and Kurt Zouma should Terry fail to make it.
"I have complete trust in Cahill and Zouma," he said. "That's why, in a fundamental match for us on Tuesday, I left Zouma out after good performances to play Gary and show Gary that confidence. They are ready."
Brazilian Ramires is also doubtful with a slight muscular injury picked up in training in Israel.
After winning their last two games, against Norwich City and Maccabi, Mourinho was asked if he felt his struggling champions, still 15th out of 20 in the table, had turned a corner.
"No," he responded. "I think Chelsea is a big club and big clubs have difficult moments. Big clubs cope with difficult moments and try to build again, to have good moments again.
"Every point between now and the end of the season can make a difference. We've lost so many already, now we have to fight even more."
Mourinho poured cold water on stories that he will be seeking to buy a high-profile striker in the New Year transfer window.
"I'm not focused on the market because I think about going with the same players," he said. "I don't think we go to business. Still one month but I don't think so."
(Writing by Ian Chadband; Editing by Tony Jimenez)
