"It's a good question. I don't know," said Farah, when asked on BBC radio if he was going to be fit for the Games.
"Hopefully I should be good. I have missed a bit of training, but we'll make a decision further down the line."
The 31-year-old is due to run in the 5,000m and 10,000m.
Farah was admitted to hospital in the United States with abdominal pains at the start of the month and has had further tests in the United Kingdom.
He said team doctors have given him the all-clear to return to training but he has not confirmed whether he will run in his next scheduled race, over two miles at the London Anniversary Games on Sunday.
The 5,000m final is on July 27 and the 10,000m on August 1.
- Sports & Recreation