A consultation document issued at the time suggested a base price of 45 Pence per unit, but the government has yet to announce its final verdict.
Home Secretary Theresa May, Communities Secretary Eric Pickles and Education Secretary Michael Gove were reported to be high-profile opponents of the proposals.
Former Health Secretary Andrew Lansley warned the law would "more likely to have a bigger proportionate impact on responsible drinkers who happen to be low-income households".
The report stirred an angry reaction from within the Conservative ranks and the Labour Party.
Backbench Tory Sarah Wollaston took to Twitter, writing: "Very concerned about suggestion that minimum pricing to be dropped from alcohol strategy."
Shadow home office minister Diana Johnson said: "Theresa May and David Cameron have announced a minimum alcohol price twice in the last 12 months."
"Now we hear reports the Home Secretary has changed her mind on her own policy and wants to U-turn."
"This is weak leadership and weak government. The Home Secretary and the Prime Minister said this measure would cut crime and prevent alcohol abuse. What's changed?"