Mike Brey won’t be Maryland’s next basketball coach, a source close to the process of finding Gary Williams’s successor said Sunday.

Brey was crossed off the list of potential candidates Sunday before having a conversation with Maryland Athletic Director Kevin Anderson because he’s committed to remaining at Notre Dame following the Irish’s 27-7 season, which earned him Big East coach of the year honors, the source said.

With Arizona’s Sean Miller agreeing to a contract extension that was announced Saturday night, that means Maryland’s search will launch into a new phase on Monday, focusing on a short list of names that haven’t necessarily been bandied about in the frenzied media reports that followed Williams’s stunning announcement last week that he was retiring after 22 years as coach of his alma mater.

“I don’t believe it’s going to be a long process,” Anderson said on Sunday. “We’re doing our due diligence, making sure we’re going to hire the right person.

“We’re just not going to panic and pick somebody who might not be the best fit for Maryland. We’re going to look at the whole person. Here’s what I’m looking for: Someone with most, if not all, of the qualities Gary Williams possessed.”

On many counts, Pittsburgh’s Jamie Dixon seemed to be that coach. Dixon, who has a close relationship with Anderson, was at the top of Maryland’s initial wish list. But like Brey and Villanova Coach Jay Wright, Dixon didn’t pursue the opening because of his loyalty to his present employer.

“I’m flattered by the interest,” Wright said in an e-mail exchange early in the process, “but I love Villanova!”

Williams’s decision to retire came a shock to those close to him, including his players, many of his peers and Maryland officials. While he has made suggestions to Anderson about who might succeed him, Williams won’t be part of the official search process going forward.

On Monday Anderson is expected to meet with Maryland President Wallace Loh, and a search committee will be impaneled to be in position to review a short list of job candidates once they’re identified.

Williams’s retirement creates the fourth coaching opportunity in the ACC this season (following turnover at North Carolina State, Miami and Georgia Tech) and the seventh in the past two years.

Opinions differ regarding the desirability of the Maryland coaching job.

To many Terrapins fans, it’s among the top 10 or 15 in college basketball and, as such, should attract a big-name coach with a proven track record. Others note the daunting challenge posed by perennial powers Duke and North Carolina, which have combined to win 14 of the last 15 ACC championships. (Maryland snapped that chokehold in 2004).

Maryland, the 2002 NCAA champion, competes in a state-of-the art, on-campus arena, 17,950-seat Comcast Center. While average home attendance declined by 11 percent last season (from 16,792 to 14,910), Comcast Center is widely regarded by visiting teams as a difficult place to play, given the spirited support of Maryland undergraduates.

And under Williams, who thrived on upsetting favored foes, Maryland trailed only Duke in the number of ACC victories over the last 12 years entering last season, which ended with a disappointing 19-14 record overall, 7-9 in the ACC.

Williams spoke passionately during his retirement news conference about the post he was vacating, saying he couldn’t imagine a better job for a true competitor.

“The ACC has taken some knocks the last couple of years,” Williams said Friday. “But check who has won the most national championships the last 10 years. Check who has won the most NCAA tournament games the last 20 years.”

Replacing Williams presents Anderson with his second major assignment in less than eight months on the job as Maryland’s athletic director.

After a two-week search for a successor to football coach Ralph Friedgen (like Williams, a Maryland graduate), Anderson surprised many ardent Terrapins boosters by choosing Randy Edsall, who lacked broad name recognition despite leading Connecticut to a share of the 2010 Big East championship.

In replacing Williams, Anderson will be expected to move more swiftly to ease anxiety among Terps basketball fans and returning players, alike.