The Conservatives seized on the document, accusing Ed Miliband of caving in to his "paymasters' demands".
Mr Miliband hit back, saying the report was a "huge opportunity for Labour to become ... a genuine living, breathing movement."
Labour wants union members to join the party rather than affiliate through their organisations. But the report, by ex-union boss Lord Collins, said unions' share of the vote for leader could remain unchanged.
It asks Labour members: "Once individual affiliated members have had an active choice about whether to be part of the Labour Party, do you believe we would need to consider the consequences for other party structures including conference and the rules for electing leaders?"
Conservative Party chairman Grant Shapps said: "Instead of taking on the unions over fixing selections, Ed Miliband has once again backed down to his paymasters' demands."
The planned reforms have led to warnings few trade unionists will want to join Labour, costing the party up to £9 million a year as it has to fight the next election.
The report was commissioned in the wake of allegations the Unite union attempted to rig the contest for Labour's Westminster candidate in Falkirk.
Earlier this month the party announced no organisation or individual had broken any rules after "key evidence" was withdrawn.