HOUSTON -- Alex Cora was in New York on Sunday as the American League Championship Series switches cities.

The Boston Red Sox were there to meet him.

Cora, the Houston Astros' bench coach and a top managerial prospect, interviewed with Red Sox president of baseball operations Dave Dombrowski during a day off in the ALCS against the New York Yankees. Boston is shopping for a manager after dismissing John Farrell last week.

With the Astros still alive in the postseason, the Red Sox requested and received permission to speak with Cora, who is also part of the New York Mets' first round of interviews and the Detroit Tigers', sources told ESPN's Marly Rivera.

Cora, who turns 42 on Wednesday, hasn't managed in the big leagues, though he has experience as both a manager and general manager of a winter-ball team in Puerto Rico. He has a reputation as a strong communicator and a mentor for young players, and after playing for the Red Sox from 2005 to 2008, the former infielder is familiar with the heightened demands and expectations that exist in sports-crazed Boston.

"He's very sharp, sees the game in an extraordinarily deep way, has really connected well with players in our clubhouse and spent a lot of time developing relationships and being the bench-coach liaison to the clubhouse that I asked him to be," Astros manager A.J. Hinch said. "For him to be able to learn, to grow, to evolve, become a better bench coach, continue to learn the game, those are characteristics as to why he is a hot name in every opening that's coming up so far and why one day he's going to manage, whether it's now or later."

Cora has interviewed for several previous managerial openings, including with the Arizona Diamondbacks last winter and the Texas Rangers the previous offseason.

Despite winning 93 games and the AL East in back-to-back seasons, the Red Sox have a relatively young roster. All-Star right fielder Mookie Betts and shortstop Xander Bogaerts turned 25 earlier this month, while left fielder Andrew Benintendi is 23 and third baseman Rafael Devers is 20.

Dombrowski said "it will be very important" for the next Red Sox manager to relate well to young players and help develop them as future leaders of the team.

"We have a young core of players that are outstanding young talents. I think they have a chance to be championship-type players," Dombrowski said. "They're still in their growth stage. It's a great foundation for a baseball club. We do have some veterans, of course, in that mix too, but I think it's going to be very important for whomever it is to be able to relate to those youngsters and not only relate to them but help them get better as players."

Dombrowski said he was keeping a working list of possible managerial replacements even before Farrell was let go. In addition to Cora, the Red Sox are believed to be interested in former Tigers manager Brad Ausmus and longtime former Minnesota Twins manager Ron Gardenhire. Ausmus was hired by Dombrowski in Detroit and has a good relationship with Red Sox lefty David Price.

The Boston Globe was first to report Cora's scheduled interview with the Red Sox.