There was some concern that that the fast bowler would be ruled out of the series but Finn now hopes to be able to test his recovery in a three-day match for the England Performance Programme squad in Mumbai next week.
He was unfit for the first Test - which ended in a nine-wicket defeat in Ahmedabad on Monday - and on Tuesday was ruled out of the second too, after suffering a setback in his rehabilitation.
But his pace and height are seen as vital to England's chances and they are keen to keep him in India if there is a chance of fielding him during the third or fourth Tests, which begin on December 5 and December 13 respectively.
A brief statement from the ECB read "Steven Finn to remain in Mumbai to continue rehab with view to playing for EPP 27-29 Nov at DY Patil Stadium."
His absence from Friday's second Test should see James Anderson and Stuart Broad continue to spearhead England's pace attack in Kolkata, despite struggling in the opener.