The pacer was sent for a scan on his left heel.
Board first had a scan on his injury during England's second tour match in Mumbai last month, but he went on to play in the first two Tests before being dropped.
He was not a part of the playing XI in the third Test at Kolkata.
While there is little chance of Broad being recalled for the fourth and final Test, commencing on Thursday here, he remains an integral part of England's T20 side.
If Board fails to recover in time, England would also have to name a new captain for the slam-bang format.
Eoin Morgan is most likely to replace him.
The two T20 matches are scheduled to take place in Pune and Mumbai on December 20 and 22, respectively.
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