"There are signs of a little bit of a tear on the pad of the heel but I have no pain when I walk or run," Broad was quoted as saying by the Times newspaper.
"There is a little bit of pain when I slam my front foot down.
"I am looking to bowl on Wednesday and Thursday next week and if I can then get through ten overs in a one-day final next week then I suggest I will be fit for the first Test."
England play South Africa at Lord's in the first of the four tests starting on July 6.
(Reporting by Aditi Prakash in Bengaluru; editing by Amlan Chakraborty)
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