Virat Kohli scored his second century of the tour as India set a daunting 521-run target for England to win the third Test at Trent Bridge on Monday.
Kohli invited England to bat for nine overs in the last session of the day after making the declaration. But openers Alastair Cook (9*) and Keaton Jennings (13*) did well as England were 23/0 at stumps, needing 498 more to win the match.
The highest successful run chase in Test history is 418, by West Indies against Australia in 2003.
Earlier, Kohli's 23 Test century inspired India to 352-7 before they declared.
England vs India, 3rd Test, Day 3: Highlights
Kohli has scored twice as many runs as any other player this series, with his 23rd test century adding to the 97 from the first innings to take his series average to 73.33. He made 149 in the first test at Edgbaston, and is in line to return to the top of the test batting rankings above Australia's Steve Smith
Kohli also crossed the 400-run mark in this series, becoming only the second Indian captain after Mohammad Azharuddin (426) to do so against England. Overall, he is the sixth Indian batsman to achieve this feat.
A day after taking 5-28, Hardik Pandya smashed 52 off 52 balls as India closed in on the declaration on day three. Cheteshwar Pujara, resuming overnight alongside Kohli with India on 124-2, made 72.
Trent Bridge Test: Virat Kohli follows up first innings 97 with 23rd hundred
"The pitch has quickened up a bit," Pujara said. "It is a lot quicker and there is a lot of deviation. On day four, it won't be easy for them to bat."
England lead the five-match series 2-0.
England's dwindling chances of avoiding defeat in Nottingham were further hit when wicket-keeper batsman Jonny Bairstow broke a bone in the middle finger of his left hand attempting to take a catch.
Bairstow didn't return to the field Jos Buttler took over wicketkeeping duties and England didn't give an indication of whether Bairstow will be asked to bat in the team's second innings.
"Although we are a long way behind," England assistant coach Paul Farbrace said, "we showed real effort and it was important not to lose any wickets this evening."