LAS VEGAS – With the physical exam taken and an offer sheet signed, Jeff Teague had been scouring the sights of downtown Milwaukee, where the Bucks’ plan resonated with him. The Bucks let him know he would be a franchise leading guard for them, and backed up the pitch with a four-year, $32 million proposal last week. For his part, Teague did his research about the city and all but went looking for a house in readying himself.

The Atlanta Hawks pushed against the three days given to decide on his offer, and Teague grew increasingly comfortable about playing under Larry Drew once more. In his mind, it seemed the chances of a return to the Hawks had dwindled too much.

“I really didn’t think the Hawks would match it,” Teague told RealGM. “I was definitely prepared to go to Milwaukee. I was excited to work with their head coaching staff. Possibly playing for [Drew] again, it was big. I have a great relationship with him.”

Teague had made public his belief that Atlanta lacked aggressiveness to re-sign him, and still, Danny Ferry and Mike Budenholzer called the 25-year-old late Saturday afternoon. Together they delivered a message Teague wanted all along out of the organization that drafted him in 2009 and thrust him into a 2011 playoff series against Derrick Rose that he still credits as outline for his potential.

When the phone call came from the Hawks’ general manager and new coach, Teague finally heard out of them: “We want you back. It’s not something we have to do – but something we want to do.” Teague needed some time to get over what led to the Hawks matching his offer sheet, but eventually he came to grip with the process and made an unmistakable point that this won’t be comparable to when Eric Gordon had proclaimed his love for the Phoenix Suns only to return to New Orleans and be in constant speculation.

“I mean, I understand it’s a business,” Teague said. “I don’t pay attention to it, even if it might be difficult. I’m just glad I’m part of the Atlanta Hawks, glad to be back in the city I love. I love Atlanta: great people, great fans.”

The Hawks’ return of Kyle Korver and signing of Paul Millsap should be lauded moves, and they reached agreement with Elton Brand on Tuesday. Even so, the Hawks maintain interest in re-signing Ivan Johnson, a league source told RealGM.

Teague has already reconnected with summer league players about his return, received a Twitter welcome back from Al Horford, and Millsap joined him here Monday night. Most of all, Teague understands the importance of cultivating a foundation with Budenholzer – a point guard-coach relationship that both know needs to be built on trust. They’ve already started communicating back and forth since Teague re-signed, and Budenholzer has laid out a plan centered on flourishing his game – passing and scoring – within a deeper team.

“I’m excited about coach Bud,” Teague told RealGM. “We’re developing a relationship right now. He’s a really good guy, and a lot of people have been telling me he’s a great coach. I’m excited to work with him.

“We’re going in the right direction. We’ve got a lot of talented guys on the roster, a lot of good character guys willing to work. Now we’re becoming a better team."