On the eve of the match at Nagpur's VCA Stadium, England learned that Stuart Broad will definitely be unfit and Finn may also be unavailable.
The tourists, 2-1 up with one to play as they bid to become the first English side to win a series in India since 1985, are therefore down to three fit seamers; James Anderson, Graham Onions and Tim Bresnan.
Onions has not played in the series and has not featured for England since the victory over the West Indies at Edgbaston in June, while Bresnan was dropped after going wicketless in the nine-wicket defeat in the first Test.
Broad was ruled out of contention today because of his bruised left heel, but may still be available for next week's two Twenty20s.
England's Twenty20 captain had been unlikely to feature initially in any case due to his poor form in the first two Tests, where he failed to take a wicket, which led to him being dropped for Finn, but his replacement's ailment has now made Broad's problem more of an issue for England.
An England and Wales Cricket Board statement revealed that Finn, who took four wickets in the seven-wicket win in Kolkata, and Broad were sent for a scan on Tuesday. It added that Finn would not train today and a decision regarding selection would be made this morning.
Broad first suffered his heel injury in a tour match in Mumbai last month. After suffering more discomfort at net practice on Tuesday he was sent for a second scan which showed exactly the same as the first one he underwent five weeks ago.
Alastair Cook, the Test captain, confirmed the news at his press conference at the VCA Stadium today. "Stuart is out of this Test match," he said.
"His scan has showed a bruised heel and we'll assess him over the next day or so to see what happens with the Twenty20. We'll know a bit more when it settles down."
Meanwhile, two unnamed senior cricketers in the India team denied any rift between MS Dhoni, the captain, and Gautam Gambhir, the opening batsman.
A report on the CricketNext website published remarks supposedly by an insider - also unnamed - who said: "What [has] irked Dhoni was Gambhir playing for himself and not for the team."
But one senior player told the Rediff website: "It is a made up story, just to get publicity for their website. Dhoni and Gambhir had a good laugh about it. There is no rift between them."
Follow us @SprtNationalUAE