The amendment was widely seen as an attempt to water down next week’s parliamentary motion, which proposes an “in or out” referendum on whether or not the UK should remain a part of the EU.
The amendment would instead suggest that the government seeks to alter the terms of membership, and then offer a referendum on the new terms.
All three major Westminster parties are expected to order their MPs to vote against the current motion on Monday. Yet a rebellion among Conservative MPs could embarrass Prime Minister David Cameron.
“I believe we will see a record rebellion,” said Richmond Park and North Kingston MP Zac Goldsmith, one of 76 signatories to the motion.
“Membership of the EU is no longer a settled political decision,” added Conservative MP Douglas Carswell. “It is now acceptable to challenge it.”