Not only did Griffin hear his teammate's words, he also agreed with them.
"[Paul] has a huge role on this team," Griffin said Thursday in an interview with ESPNLosAngeles.com. "He's been the guy who has closed out a lot of games late for us.
"But in my mind, this is the year I need to step into that role and really help him shoulder that load. I'll be right there with him at the end of games, being the guy that he can always count on."
Griffin, 24, has developed into one of the best power forwards in NBA during his first three seasons, but he has yet to advance past the second round of the playoffs.
Griffin made his third straight All-Star team last season, but his season averages in scoring (18.0) and rebounding (8.3) fell off slightly from his career averages (20.4 points, 10.4 rebounds), as he played nearly three fewer minutes per game during the regular season, at 32.5, in an attempt to stay healthier for the playoffs.
Griffin's assists rose to 3.7 per game in 2012-13 from 3.2 in 2011-12, while his steals rose from 0.8 to 1.2 per game over the same period.
"Blake is one of those guys where his age has nothing to do with anything," Paul said in a phone interview with ESPNLosAngeles.com on Aug. 6. "People may say he's a young guy, but he's been special in this league, he's been an All-Star. His voice carries a lot of weight, and I think our team will definitely go as Blake goes.
"He's our guy, and he's good enough to do so."
Griffin was in Los Angeles on Thursday and back at the Clippers' training facility attending a promotional event for Red Bull's midnight basketball tournament. He's been traveling for a large chunk of the summer, both for business and vacation, but said he's been able to heal completely from an ankle injury that limited him in the Clippers' first-round playoff loss to the Memphis Grizzlies, and has worked on his face-up game.
"To be honest, I'm more excited about this upcoming season than I've ever been," Griffin said. "My workouts with [shooting coach] Bob Thate and our coaches have been geared around figuring out how I'm going to be used this season.
"I'm doing a lot of stuff at the elbow, a lot of shooting. One of the things [new coach Doc Rivers] said to me was, 'I don't want you to be afraid to go 0-for-15.' In other words, just have the mindset of a shooter. And with the work I've done this summer, I'm starting to get that confidence and think like a shooter."
Griffin shot 53.8 percent from the field last season but just 34 percent on shots from 16 to 23 feet, according to Hoopdata.com. He did noticeably improve his shooting from 10-15 feet, from 27 percent in 2011-12 to 40 percent last season.
Griffin thinks he still can make much improvement, however, and that when he proves he can hit a face-up jumper, it will change the way defenses play him.
"We've been working on a lot of face-up stuff in the post," he said. "I'm definitely going to be used differently this year.
"This summer has been so great for me. I've had a completely healthy, full summer to be able to work with our coaching staff, once I got over the ankle thing. This summer has been huge for me, and it's one of the reasons I'm so excited about next year."
Griffin said he sat out about a month after the Clippers' season ended to rest and let his badly sprained ankle heal.
"It lingered for a little over a month," he said of the ankle injury that hampered him in Games 5 and 6 of the Memphis series. "But by the time I was back to working out, it was fine. I won't really take that much time off the rest of the summer. I want to keep the training going."
The relationship between Paul and Griffin hasn't always been perfect in their two years as teammates. Their visions for how the team should be playing haven't always meshed.
But after spending a significant amount of time together this summer -- traveling to Asia as part of a tour for Nike's Jordan Brand and filming a national commercial for Foot Locker -- Paul says their bond, and understanding of each other, has deepened.
"It's been a great summer for us. I think we've both had an opportunity to grow," Paul said. "As you get older you realize it's all about winning, and I think we both realize we really need each other in order to do that."