The Archdiocese of New York wants to spend more than 300 million US dollars on settling abuse claims.
As the "New York Times" reported on Monday (local time), the money will be used to compensate around 1,300 people who were sexually abused as minors by priests or church employees.
The archdiocese and the lawyers of those affected have reportedly agreed on the main features of a mediation process in order to resolve the compensation issue amicably.
One of the lawyers spoke of a "step in the right direction".
However, no binding agreement has yet been reached.
Cardinal again asks for forgiveness
"As we have repeatedly recognised, the sexual abuse of minors brought shame on our church long ago," New York Cardinal Timothy Dolan is quoted as saying. "I again ask forgiveness for the failure of those who betrayed trust in them by not ensuring the safety of our youth."
The archbishop said the archdiocese had made "a number of very difficult financial decisions" to raise the more than $300 million needed for a settlement.
These included employee layoffs and the sale of real estate, including its longtime headquarters on First Avenue in Manhattan.
New York is not the only diocese in the USA that is in dire financial straits due to numerous abuse claims.
The Archdiocese of New Orleans has now confirmed that a settlement has been reached in court with those affected.
According to the agreement, around 230 million dollars are to be paid to hundreds of people. Archbishop Gregory Aymond announced that he was "glad that this process is now over".