The injury forced Terry, 29, to miss Sunday's 3-0 defeat by Sunderland and he has also pulled out of England's friendly against France on Wednesday.
A Chelsea source told BBC Sport: "It could be months [until he's fit], although that's the pessimistic view. We don't know the root of the pain."
Fellow defender Alex has been ruled out for up to two months.
Chelsea revealed that the Brazilian centre-back will be out for "approximately six to eight weeks" to undergo exploratory arthroscopic surgery on his injured knee in the coming days.
Having already missed the club's matches against Fulham and Sunderland, on Tuesday Alex withdrew from the Brazil squad set to play Argentina.
Both assessments are likely to come as a blow to Chelsea manager Carlo Ancelotti, who also has persistent injuries to midfielder Frank Lampard to contend with while Ivorian striker Didier Drogba is playing on despite a recent bout of malaria.
Regarding Terry, the Chelsea source also told BBC Sport: "He can't keep struggling, so he has to get to the source of the problem."
606: DEBATE
If the injuries remain long term, then this may end up being a transitional season...
Still Got the Blues
The Londoner is already seeing a variety of specialists in an effort to cure the injury but so far nobody has identified what is wrong with the centre-back.
A Chelsea spokesman said: "John reported for training this morning. He met with club doctors and the medical team and discussed plans to continue seeing various specialists to try to find a solution to the nerve problems he has been experiencing in his right leg."
The injury has been troubling the defender since the end of last season and, despite resting for three weeks between the end of the World Cup and the start of the Premier League season, the problem has not cleared up.
Terry told the Daily Mail: "It has been manageable up until the last two weeks but when we played Fulham I stretched to win the ball against Clint Dempsey and it got a lot worse.
"It is at a point where I can't carry on with it. I used to be able to make it through games because the adrenaline gets going and you blank the pain out, but now there really is no decision to make.
"After games I am in agony and not sleeping at all. I used to play with pain at seven out of 10. Now? It's 10 out of 10. I need to take a few weeks rest, see a couple of specialists and solve the problem.
"People are saying it could be my posture, but nobody really knows. Every time I jog or warm up, I don't feel right. It has been that way for a while, but this is different now.
"Other players have recommended guys, and I've seen a couple already, but it is just a question of finding one who can solve the problem.
"Any ideas anybody has had, I've tried them. There are guys in London who can do nerve tests on machines, and guys in Italy who look for problems higher up the body.
"That is where I am at right now, just trying to find out what is wrong."
Imagine that centre-back pairing that got torn apart by Sunderland against us in December!
Thu Jan 21 2021, 20:01 by BazSpur
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