SAN DIEGO -- With the Astros set to soar past the luxury tax threshold for the first time in their history with a payroll north of $208 million in 2020, owner Jim Crane said Monday the team remains fully capable of being able to fill its needs this winter despite the payroll limitations.

The Astros, who lost in seven games in the World Series to the Nationals following a 107-win regular season, hit the Winter Meetings on Monday looking to add at least one starting pitcher and a reliever and identify a starting catcher. Even without making any moves of significance yet this winter, the Astros’ payroll has skyrocketed in part because of recent extensions given to second baseman José Altuve, third baseman Alex Bregman and pitcher Justin Verlander and the July trade to land pitcher Zack Greinke.

“I think anybody can do the math on where we’re at,” Crane told MLB.com via phone Monday. “We’ve got a few holes. We need to sign a catcher, need a few arms -- bullpen, maybe a starter. When you look at those ingredients and look at where we’re at, more than likely that will put us over the luxury tax.”

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That means the Astros will have to pay a 20 percent tax on the amount they exceed $208 million. If they exceed the luxury threshold by $20 million to $40 million, they would have to pay an additional 12 percent tax. Re-signing free-agent pitcher Gerrit Cole would almost certainly push Houston past the second threshold, but it doesn’t appear Houston has much chance of re-signing the right-hander.

Crane said shortly after the World Series the club would make a run at re-signing Cole, who’s being pursued hard by the Yankees, Dodgers and Angels. The Nationals re-signed World Series MVP Stephen Strasburg for a record $245 million over seven years Monday, and Cole is likely to land a contract north of that.

Astros president of baseball operations and general manager Jeff Luhnow arrived in San Diego on Monday but wasn’t available to reporters.

“We said we’re going to check in [on Cole] and we will check in,” Crane said.

Booming revenues following three consecutive 100-win seasons, including a World Series title in 2017, have put the Astros in position to push their payroll higher than ever before.

“Because of the support we’ve had with the fans and the sponsors, we’re comfortable where we’re at and we knew we’re going to be there and it’s not a big surprise,” Crane said. “We want to put a good product on the field, and we’ve got a good nucleus with a very good team. We just want to make sure hopefully we get back to where we were last [season].”

Houston’s rotation will return Verlander, Greinke and Lance McCullers Jr., who missed all of last season following Tommy John surgery. The Astros could use a veteran arm or two behind that while they gauge if younger pitchers like Jose Urquidy, Forrest Whitley and Cristian Javier are viable options for 2020.

Like last year’s signing of Wade Miley, the Astros will be looking to mid-level starters rather than shopping at the high end of the market. Their best bullpen addition could be bringing back steady right-hander Will Harris, who’s a free agent for the first time. Robinson Chirinos, who caught all of Verlander’s starts last season, and Martín Maldonado are both free agents and one of them could return. The club also has interest in free-agent catcher Jason Castro.

Houston’s nucleus remains strong, at least for one more year, with all of their key offensive players returning, including Bregman, Altuve, Carlos Correa, George Springer and Michael Brantley. Outfielder Jake Marisnick was traded to the Mets last week to free up some money.

“I think there’s no doubt we’ll still be the favorites in the division just because of the nucleus we have and the bats we have,” Crane said. “We’ve got two or three or four pretty good pitchers, front-line pitchers. I think if anybody does the math, we would be favored to win the division.”

The Astros, of course, are being investigated by Major League Baseball following allegations the club used cameras to steal signs during the 2017 season. Crane said the ongoing investigation -- and any subsequent penalties -- have no bearing on how the club proceeds this offseason personnel-wise.

“The investigation with MLB, we’re fully cooperating,” he said. “And when they’re done and whatever findings they have, then we’ll be happy to talk about those when the time comes.”