On Tuesday night, Lakers President and Governor Jeanie Buss said she'll hold him to that.
"Yeah, of course," said Buss at the 11th annual Lakers All-Access event at Staples Center on Tuesday night. "But I don't see why -- given the resources, given our legacy, given who our head coach is, who our front office is -- [we'll have] any problem."
Jim Buss announced his deadline to the six Buss siblings, primary owners of the franchise, vowing the Lakers will advance at least to the Western Conference finals within a few seasons.
"It was a private conversation with our family but I understand why he said it. I mean, I don't understand why he said it but I don't think it'll be a concern," said Jeanie Buss. "I think he presented a challenge to himself, but I don't know why he made that public.
"'We'll be contending,' that's what he said. 'We'll be in the Western Conference finals within three years.' I think as long as you have Kobe Bryant on your team, anything can happen in the playoffs."
Of course Bryant has just one year left on his contract after this season. The Lakers are still in search of their next star.
In the meantime, Jeanie and Jim Buss will work together, trying to return the team to prominence.
The transition since the team's patriarch, Jerry Buss, died in February 2013 after a long battle with cancer, has begun to settle into a working norm. Jeanie Buss said she still trusts her father's plan on how the Lakers should operate.
"That's how my dad envisioned it. My dad, being the visionary that he is," she said. "Any time you have a change of leadership in an organization, everything kind of shifts."
Jeanie Buss runs the business side of the organization and Jim Buss is in charge of basketball operations. Ultimately Jeanie Buss, as governor, has the final say.
"We have our comfort level in that he's doing what his strengths are, and he knows, whatever he needs, he just has to pick up the phone," she said. "He has a vision of what Laker basketball should be and that's what he does. I can't tell you the difference between the triangle offense and the Princeton offense."
"My brother has skills that are better than me," continued Jeanie Buss. "He could always beat me in Monopoly. I respect that he knows what's going on."
"It's important, especially for the high-profile players ... that they know who the key players are in an organization, both on the basketball side and on the business side," she said. "I'm part of the overall message, but when it comes to basketball, they excuse me from the room. I'm not part of the basketball discussion."
Buss said she understands why Anthony chose to return to New York. She's confident the Lakers haven't lost any luster and are still are the premier NBA destination.
"Laker Nation would embrace them and they would be immensely popular," said Buss. "In terms of a platform for a player, you couldn't ask for anything better than this ... the dedication of our resources, to all things basketball, to making sure the players get the best treatment, care, support, coaching training facilities, everything.
"Certainly the connections they can make in this town will lead them to other opportunities during their basketball career and after. I think that's the story we can tell in terms as a destination, but it has to be the right fit for the player, and the organization."
In the meantime, Buss is trying to be patient as the Lakers struggle in what looks to be their second consecutive season without a playoff bid.
"We're just in a cycle now. We're going in the right direction," said Buss. "Every fan wants to win every year, that's how my dad was. It would be nice to be able to do that every year, but I think Lakers fans know, as long as they see progress, and steps going in the right direction, they'll be patient."