Instead, he says he wound up being a big reason why Kemba Walker chose to be Irving's replacement as the star point guard of the Boston Celtics, thanks to a sales pitch he gave Walker during their time together in Paris earlier this summer as part of a Jordan Brand event.
"I'm very excited," Tatum said. "I think I had a big part with him coming here. I was with him in Paris.
"I never told him to come, but I told him I would love for him to join the team and told him how it was. Obviously everybody has to do what's best for themselves, and I'm happy for him."
So, if Tatum didn't tell Walker to come, what did he tell him?
He said he sold Walker on what it is like to play in Boston, the team's fans and how the organization would treat him.
"I just told him about Boston, the city, the atmosphere, our fans, the culture, the coaching staff. I answered all the questions he had," he said.
"I'm excited, and just ready for the season to start and everybody to be around each other and build some chemistry and just get it going."
Tatum's remarks, which came at a pop-up event for his new cologne, come on the heels of Walker saying similar things to ESPN's Jackie MacMullan during a sitdown interview last month, in which he talked about how those conversations with Tatum helped spur Walker to choose to join the Celtics after spending the first eight years of his career with the Charlotte Hornets.
"We spoke for quite some time," Walker told MacMullan. "When we left Paris and the days went on and [free agency] came and I made my decision, a lot of it was because of him.
"[We talked] about the city, about the fans, the atmosphere, Coach Stevens, some of the players on the team, how things went last year and stuff like that.
"[But] not once did he say, 'Come [here].'"
Before Tatum can play with Walker on the Celtics, however, he's hoping to join him as part of Team USA's entry in the FIBA World Cup, which begins Aug. 31 in China. After a series of high-profile defections from the training camp roster in recent weeks -- including James Harden, Anthony Davis and Damian Lillard, among others -- Walker is expected to be the focal point of Team USA's entry under Gregg Popovich, who will be at the helm for the first time since taking over for Mike Krzyzewski.
"I played [with the] USA three times when I was in high school, and it's an honor to play for the country and to be along other great players," Tatum said. "That's what I'm most excited for, being around other guys and competing in practice and coming together for a greater purpose.
"I think that's pretty cool," he added, of the possibility of four Celtics being part of this year's team. "I know a lot of people dropped out and I feel like everything happens for a reason, so hopefully we all four make it and start some early chemistry for the season."
Team USA -- and the World Cup entries, in particular -- have served as jumping-off points for young players in the past to take the next step forward in their careers. Kevin Durant and Stephen Curry, for example, played big parts in Team USA's win at the 2010 World Cup in Turkey, as did Irving, Harden and Klay Thompson in the 2014 edition of the tournament in Spain.
The high-profile defections have increased the chances of Tatum making this year's team, and he sees the same kind of opportunity for himself to use the tournament as a chance to take a significant leap heading into next season -- the kind Boston hopes Tatum will make, as it tries to remain relevant in the Eastern Conference after losing both Irving to the Brooklyn Nets and Al Horford to the Philadelphia 76ers in free agency this summer.
"It's a great opportunity and just build from it and carry on into the season and have a great season individually and as a team," Tatum said. "I'm really looking to take a bigger jump. Be more vocal, be more of a leader. Just be a better version of myself."
Tatum and Irving grew close over the past two years, thanks in part to both sharing an alma mater -- both played one year at Duke before entering the NBA -- and an agent in Jeff Weschler. While things changed this summer, Tatum said he and Irving still talk regularly, and that his departure from Boston didn't impact their friendship.
"We still keep in touch," Tatum said. "That's like family. We talk often. Nothing in particular, nothing specific about last season, just friend talk.
"I'm all for guys doing what's best for them. It doesn't change the dynamic of our friendship."
The departures of both Irving and Horford was the final blow to what was an ugly season for the Celtics, who entered the year as the favorites to emerge from the Eastern Conference -- only to finish fourth in the East and get run out of the playoffs in five games, including four straight losses, by Giannis Antetokounmpo and the Milwaukee Bucks.
Those struggles have led many to ask varying versions of the same question: How could such a promising season go so differently than anyone -- including the Celtics themselves -- ever could have guessed?
Tatum said that even now, three months later, he doesn't have an answer.
"I don't know," Tatum said. "We've all been asked that question a lot.
"There's no specific answer, but I kind of feel like everybody is ready to leave last year behind us. It's a new season, we've got a new team, new guys ... so last year is behind us."