Nearly two months after he was hired to remake the Giants, and three weeks after the winter meetings, president of baseball operations Farhan Zaidi has added one big-league player to the roster, ambidextrous reliever Pat Venditte.

Pitchers and catchers report to spring training in less than six weeks, yet the Giants hardly look different than the team that endured a second straight losing season in 2018.

Fans are restless, and Zaidi understands. He recognizes the fans want him to get things done in a big way, but in a New Year’s Day phone interview, Zaidi suggested he is taking a different course, trying to be patient in a slow-developing market and negotiating as many moves as he can to improve a team that is not one or two players from contending.

“I will say, unequivocally, that our player-acquisition strategy is not driven by who we think is a, quote-unquote, brand name and who would be perceived as a big-splash acquisition,” Zaidi said. “We want to acquire players who make the team better in 2019 and beyond.

“More generally, we’re focused on which guys we think are productive players for us, and not which guys grab the most attention on the ESPN ticker.”

Perhaps that was Zaidi’s way of hinting the Giants need not manufacture Bryce Harper jerseys for the team store, just as they did not have to stock any Yusei Kikuchi gear.

Many of the faithful had hoped the Giants would sign the 27-year-old Japanese left-hander to boost the rotation. Kikuchi had signaled his interest in San Francisco as well.

The feeling was unrequited, and on New Year’s Eve, Kikuchi agreed with the Mariners on a complex contract that guarantees him $56 million over four years, and ultimately could be worth $106 million over seven years.

Zaidi would not comment on Kikuchi, just as he will not discuss any free agents remaining on the market or specific trade ideas.

However, like many teams deliberating over Japanese players, the Giants were thought to be split internally on the pitcher’s value and potential durability, enough to make them wary of adding a $14 million annual commitment to an already pricey rotation.

More broadly, the decision to pass on Kikuchi provides further evidence that the new administration does not think it can set the Giants on a proper course by grasping at a few shiny baubles on the market.

Zaidi pledged to improve the Giants by making “one good baseball move after another,” which might mean more players on the Venditte end of the scale who give manager Bruce Bochy flexibility between the lines in 2019 and the front office the maneuverability to complete a longer-term turnaround.

Zaidi is hamstrung by big contracts for several underperforming or injured players who have partial or full no-trade clauses, which makes them hard to deal for the younger big-leaguers or prospects who ultimately will lead the Giants back to serious contention.

The Giants have attempted to sign free agents who went elsewhere, with Zaidi acknowledging that “not everybody we are interested in is going to have us high on their list.”

Some of that is geography, and some of it is the players’ perception that they can win sooner if they go to the Astros, Yankees or other perennial playoff teams. On the other hand, Zaidi said he has heard from many players (or their representatives) who still believe in the core of the Giants’ roster, who like playing at AT&T Park and would sign with San Francisco.

The question is, when?

Like last winter, the trade and free-agent markets are slow. Harper is holding up outfield movement to some degree.

The Giants’ best hope for acquiring young, big-league-ready players — short of trading Madison Bumgarner — is dealing attractive and relatively inexpensive relievers such as Will Smith and Tony Watson. But the Giants are waiting on that market to settle, too, as teams pursue big free agents like Craig Kimbrel, David Robertson and Adam Ottavino.

Zaidi still sees a “deep” pool of free-agent pitchers and outfielders.

Available outfielders, the Giants’ biggest need, include Avisail Garcia, Adam Jones, Nick Markakis, A.J. Pollock (not likely for the Giants because of his qualifying offer), Marwin Gonzalez and Derek Dietrich. The last two fit Zaidi’s profile for versatility because they play the infield as well.

The Giants’ front-office overhaul wrought expectations that Zaidi would make changes that largely have not happened yet.

“I think that’s fair,” Zaidi said, before insisting he is not sitting on his hands.

“From a timing standpoint, plenty of deals get done in January and some deals get done in February,” he said. “It does seem that offseason activity gets later and later every year. I don’t feel any pressure to get something done until and unless we think it’s the right thing to do.

“We’re very motivated, obviously, to fill those needs and get better. But we don’t want to get into that mode of desperation, which will hurt us more in the long run.”

Henry Schulman is a San Francisco Chronicle staff writer. Email: hschulman@sfchronicle.com Twitter: @hankschulman