Anthony DeSclafani is returning to the Bay. The Giants on Monday signed the right-hander to a three-year deal worth $36 million, and it could be just the first of several moves to strengthen the team's pitching staff.

While DeSclafani's signing was official, the club was nearing a deal to bring back left-hander Alex Wood on a two-year contract, a source told MLB.com's Jon Paul Morosi. The San Francisco Chronicle also reported the team was making a "strong push" to sign free agent right-hander Alex Cobb. The club did not confirm either move.

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"I know there's rumors out there about other guys we're talking to, obviously," said Farhan Zaidi, Giants president of baseball operations. "We've talked a lot about the fact that we're going to be active in the starting pitching market.

“I won't comment on anyone specifically, but I will say we've talked about this a lot over the last few years: We're not sort of shopping for a five-man rotation, we’re shopping for 162 games started. So that can take on different forms. But I imagine that even after the signing, we'll continue to be in that space."

DeSclafani, 31, is coming off a one-year, $6 million contract with the Giants that coincided with the best season of his career. The right-hander set career bests in wins (13), ERA (3.17), FIP (3.62) and WHIP (1.09). He also tied for the Major League lead with two shutouts for a San Francisco club that won a franchise-record 107 games and the National League West title.

The Giants recently declined to give DeSclafani a qualifying offer, preferring instead to work out a multiyear deal with him, something the two sides discussed during the 2021 season.

"He obviously had a really nice year for us," Zaidi said. “You know, beyond his individual stats, we were 21-10 in games that he started. So the team had a lot of success when he took the ball, which obviously is of the ultimate importance.

“His interest was in doing a multiyear deal, and we actually think we're going to get a sort of really comfortable and secure pitcher in Anthony now that he's on a multiyear deal. So it just seemed like [a multiyear deal] was the best fit for both parties."

DeSclafani’s season had a bitter finish, when he recorded only five outs in his NLDS Game 4 start against the Dodgers, but his year exceeded expectations (save, perhaps, an astute member or two of the Giants’ front office) given that he struggled to a 7.22 ERA during the pandemic-shortened 2020 campaign.

DeSclafani cut down the walks from that rough year, returning his strikeout and walk rates to nearly identical levels as his career averages. One of his biggest strengths was limiting the long ball, as he allowed 1.0 home runs per nine innings -- his lowest rate since ‘15. He did so primarily with an old-school sinker/slider combination that held batters to a .187 average, the third-best figure among pitchers who ended at least 100 plate appearances with those pitch types.

The Giants feel like there might even be more room for DeSclafani to grow.

"At the end of the day, if we get three seasons from Anthony like his 2021 season, we'll be pretty happy with that, because he had a really strong year," Zaidi said. "But talking to Anthony and talking to our pitching coaches, there's still room for improvement. And that's obviously a theme in our clubhouse and in our organization.

“There's a constant strive for improvement, and there are things that we think he can do better -- continue to evolve his mix and improve, particularly against left-handed hitters. And we have some ideas on how he can do that."