The Labour, Green and Maori parties are strongly against the bill in its present form, but the Herald understands Mr Power has won the support of United Future leader Peter Dunne and Act MPs Hilary Calvert, Heather Roy and Sir Roger Douglas by removing the disclosure regime from the bill (Act MPs are not "whipped" to vote as a caucus).
The ability of a judge or jury to infer a greater likelihood of guilt from non-compliance would also be removed.
A new clause would allow the Rules Committee, a panel of legal experts chaired by Chief Justice Dame Sian Elias, to decide if a disclosure regime should be enforced, and if so, how.
The committee has responsibility for procedural rules in the court system, and relies on advice from judges, lawyers and other interested parties.
Dr Bill Hodge, an associate professor of law at Auckland University, said delegating control to the committee would be "unusual" because Parliament usually makes the law, while the judiciary applies it.
"It is a creative approach, if you're stuck with a parliamentary impasse. It's kicking for touch, in some respects, but on the other hand, it couldn't find a better place to go.
"Some judges will say, 'Thank heavens we don't get something imposed on us by the executive, who don't really understand pre-trial process', and the judges understand it better than anyone."
Labour's justice spokesman, Charles Chauvel, said the party was unlikely to support the changes.
"If it ends up passing by one vote - the abolition of the right to silence and a substantial amendment to the Bill of Rights Act - then I'm happy for that to be his legacy as Minister of Justice, but I'm not sure it's a legacy I would want."
Act MP Rodney Hide said he remained "totally opposed" to the bill.
"I regard the right to silence as a fundamental right, as well as freedom of speech, and I'm shocked that a centre-right Government is proposing to remove it."
A spokesman for Mr Power said negotiations were continuing.
It is understood Mr Power wants to pass the bill into law before the House rises on October 6.
BREAKING IMPASSE
* The Criminal Procedure Bill would remove the right of an accused person to remain silent and not have that held against them.
* The bill has stalled, as it did not have the numbers to pass.
* Justice Minister Simon Power has won enough support by proposing to remove the controversial provision from the bill and leave the issue up to the Rules Committee - a group of judges and legal experts.