Talk about a good first impression.

Carmelo Anthony says he’s off on the “right foot’’ with new Knicks coach Jeff Hornacek, who surprised the All-Star by viewing his workouts.

Anthony campaigned after the season for Knicks president Phil Jackson to seek an alternative to interim coach Kurt Rambis, who will stay on as the lead assistant.

“He came to see me work out a couple of times, which was surprising,’’ Anthony said Monday at the US Olympic Team press conference in Harlem. “My head coach is in there, sitting there waiting to watch me work out. That was good feeling just to see the energy and vibe was a lot different. For him to take that step and want to have that conversation with me, wanting to start off the relationship on the right foot, I accepted that.

“But how we’re going to play, we haven’t discussed basketball. He’s trying to get his situation acclimated living in the city, family. It’s a big adjustment, but I’m a big supporter.’’

Anthony was effusive about the Derrick Rose trade as “the splash’’ the Knicks needed to make before free agency because of the competition with every team owning cap space. And Anthony put to rest rumors Rose never spoke to him during his free-agent recruiting visit to Chicago two years ago — an indication he was ambivalent about Anthony’s potential signing. The reports had Rose working out at the facility during Anthony’s visit and then declining to attend the recruitment dinner.

“I saw him,’’ Anthony said. “That’s you guys making those stories up. I see his spirits are up. I’ve talked to him. He’s focused, [but I’ll] leave him alone and let him get back into the flow of things. It all happened so fast for him.”

Though he dined with Kevin Durant last weekend, Anthony will speak to more realistic free agents.

“I’ve got a list,’’ Anthony said. “There’s certain guys that’s on the list I feel we have a great shot at acquiring. It’s going to take work. Derrick was a great first step.’’

Anthony, after giving pause in May, admitted it was a tough decision to join the Olympic Team because of the health concerns in Rio, specifically the possibility of contracting the Zika virus. He said he consulted a lot of medical people, including from the Knicks. The Olympic team will gather in Las Vegas to begin training camp July 18 before the Summer Games begin in August.

“It was a very difficult decision to make kind of taking everything into consideration, going over safety in Brazil, the economy,” Anthony said. “A lot of things came into play. The way I look at it, I was training anyway, why not train with the best.”

Outside of Durant, Anthony is the biggest name on the squad as luminaries such as buddies LeBron James and Chris Paul backed out, as well as Stephen Curry and Russell Westbrook.

“You can downplay the Zika as much as we want,’’ Anthony cautioned. “Nobody has answers how to control it. All those things came into play. I had to sit down with family, talked to numerous doctors out there, put it in perspective from a basketball standpoint. I have an opportunity to win a third gold medal. I look at it as a legacy thing, too.

“We don’t have as many big-name guys as we have before, but they’re hungry,’’ Anthony added. “They want to play.’’