The Boston Red Sox are in on everybody.

OK, that’s a slight exaggeration. But it’s not stretching things to say the Sox are taking a close look at virtually every free-agent pitcher available.

They should be. They’re one of the flagship teams in Major League Baseball and are coming off a historically bad season. They are some $30 million under the collective bargaining tax threshold. They reset their tax rate to zero last season. The Red Sox did not become a small-market team overnight.

“They’ve been relentless as far as exploring the market and exploring everything,” said Boston Manager Alex Cora. “If you hear a rumor about the Red Sox, that they’re in on this guy… yes. We’re doing our homework. We’re trying to be better.”

When it comes to pitching, the Red Sox have to be better. A lot better. They need a better rotation. A better bullpen. A lower ERA.

That won’t be hard. Boston’s 5.58 ERA in 2020 was the worst in the history of the franchise. By half a run.

Let that sink in for a second. And don’t, for a second, think that the Sox are not keenly aware of how much pitching help they need.

That’s why the Sox are being linked to Jake Odorizzi. And Corey Kluber, Rich Hill, and Tomoyuki Sugano.

And just about any free-agent reliever you can think off. And a dozen others who are currently on teams but could be traded. Starters, relievers, right-handers and lefties. If they can get outs, they have a shot to call Fenway home.

“Those conversations are going on and on,” said Cora. “Not on and off. It’s on and on.”

The biggest question looming over Red Sox fans is whether or not the team can turn its fortunes around quickly. Can short-term moves return Boston to playoff contention in 2021, or will this rebuild take several years? Fans are impatient for success. The Red Sox want to be back in the hunt soon, but won’t stray from the long-term plan to make it happen.

“I think, just because of the uncertainty for society in general and for our industry, I think the winter might move slowly in some respects,” said Chief Baseball Officer Chaim Bloom last week. “That’s not going to be true across the board. … We just have to make sure we are constantly talking, constantly active, and ready to be aggressive when the situation calls for it.”

With a glut of free agents on the market, Bloom will be able to take his time and look for bargains. He’s already shown he’s willing to jump quickly, as he did with the signing of outfielder Hunter Renfroe last week. But with so many pitching spots to fill, he would be wise to get as much help as he can with the money he has available.

“This puzzle is not completed,” Cora said. “There’s a few pieces we’re missing and we’re looking for, and the opportunity will be there.”

A pitcher looking for a new team would know the opportunity is there to play a large role in the Red Sox plans for 2021 and beyond. That should make Boston an attractive landing spot. Now it’s time to wait and see how this winter plays out.

Tom Caron is a studio host for Red Sox broadcasts on NESN. His column runs on Tuesdays in the Portland Press Herald.