After interviews with up-and-coming coordinators this past week, the Giants have turned their attention to more seasoned candidates.

Former Falcons head coach Mike Smith is expected to interview for the Giants’ job on Monday, and the team confirmed that former Bills head coach Doug Marrone interviewed Saturday. There are no known interviews scheduled for Sunday and it is believed the Giants’ search will take a brief recess after Smith while John Mara and Steve Tisch attend NFL owners’ meetings in Houston next week.

By the time those meetings adjourn, there could be a new flood of possibilities in a somewhat uninspiring pool. Coordinators and assistants for squads playing in this weekend’s wild-card playoff games will be eligible to meet with teams about head-coaching positions, win or lose (although winning teams can deny the request for interviews until they are eliminated). That will make Bengals offensive coordinator Hue Jackson and Chiefs offensive coordinator Doug Pederson available for the first time in the process.

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Others such as Patriots offensive coordinator Josh McDaniels and Panthers defensive coordinator Sean McDermott — the latter a coach whom the Giants reportedly have inquired about — could become free to interview soon. After the conference championship round, only teams who already interviewed an assistant from a Super Bowl team can interview him again. And once the Super Bowl teams arrive in San Francisco for this year’s game, all interviews are closed until after the game.

Would the Giants be willing to wait that long? Mara said in a radio interview on Friday that he’d rather make his new hire “sooner rather than later, but not at the expense of finding the right guy.”

As for this crop, Smith will be the sixth interview for the Giants after Marrone, Adam Gase, Teryl Austin and a pair of in-house candidates in Ben McAdoo and Steve Spagnuolo. Gase interviewed with the Giants on Friday and was hired by the Dolphins on Saturday.

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Smith had a 66-46 record in seven seasons with the Falcons that included two division titles and four playoff berths. He was 1-4 in the postseason. He won only 10 games in his final two years in Atlanta before being fired at the conclusion of the 2014 season, and he was not in coaching in 2015.

Marrone was the Bills’ head coach for two seasons and went 15-17 before taking advantage of an out in his contract and leaving after the 2014 season. He was an assistant head coach for the Jaguars in 2015. Before that, he coached Syracuse for four seasons and had a 25-25 record and two bowl wins.

“He turned the Syracuse program around in the years that I was there,” Giants offensive lineman and Syracuse product Justin Pugh said on Twitter on Saturday. “Great coach.”

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Marrone, who some believe is the front-runner, was expected to tell the Giants during his interview that if he got the job, he would keep McAdoo as offensive coordinator. However, a source familiar with the team’s thinking told Newsday that scenario is unlikely.