The Boston Archdiocese and the parish that controls the site of the former St. William’s School are back in negotiations over locating a private Roman Catholic high school to Savin Hill, the Reporter has been told.

The archdiocese had been hoping to buy the school from the parish and lease it to officials with the private North Cambridge Catholic High School.

Talks reached an impasse last Tuesday. The archdiocese offered to pay $1.2 million for the St. William’s School site, despite it being assessed at $3.2 million. The archdiocese reportedly rejected a counter-offer from Father Jack Ahern, a pastor of Blessed Mother Teresa parish, which includes the St. William’s school property, proposing that his parish receive $1.2 million but also co-own the site with the archdiocese.

But discussions resumed with a three-hour marathon bargaining session late last week, according to Ahern, with Regional Bishop Robert Hennessey negotiating on behalf of the archdiocese. Officials from the high school, including its president, Jeff Thielman, are also involved in the talks.

Cardinal Sean O’Malley is monitoring the talks, according to Ahern. “The cardinal would like to see the school come to Dorchester,” Ahern said Saturday, while cautioning the proposal was “far from a done deal. It’s closer but not a done deal.”

As of Tuesday night, Ahern said, there had been no additional progress.

Currently being used as a storage facility, the Savin Hill Avenue school property at one time housed a parochial school that was merged with St. Margaret’s School several years ago. The combined school was relocated last year into an expanded facility on Columbia Road, and became the Columbia campus of the Pope John Paul II Catholic Academy.

North Cambridge Catholic High School, which has 265 students and has plans to expand to 400 students, is one of 22 Cristo Rey-affiliated schools across the country, a Roman Catholic college preparatory program. Many of its students are from Dorchester, Roxbury, and Mattapan.

The school also has powerful backers: Thomas P. O’Neill III, the son of the late U.S. House Speaker Tip O’Neill, is an alumnus and the chair of the high school’s board of trustees.

If the deal goes through, the school is expected to be renamed to reflect its new Dorchester location.