The thought has nothing to do with Mendenhall's running style. It has to do with the way Bettis -- a future Hall of Famer -- embraced and tutored Parker as a rookie, which eventually led to Pittsburgh winning a Super Bowl their second year together in 2005.
"JB always kept it real with me,'' Parker said glowingly. "He told me as long as I passed the blueprint on to somebody else and not be selfish, that's the only way we can have the running back tradition that we've had here.
So, yeah, it's my turn."
Parker's mentality has the potential to bring a smile to coach Mike Tomlin's face.
The Steelers' second-year coach says there is "great chemistry" and an "unwritten rule" of mentorship in Pittsburgh. The veterans teach the rookies the Steelers' way of doing things as soon as they get in the door, and the rookies are better off because of it. It's one of the reasons Pittsburgh remains one of the NFL's steadiest and most successful franchises.
Parker is not alone. Veteran receiver Hines Ward expressed the same sentiment about his relationship with Pittsburgh's second-round pick, Limas Sweed. Ward sat out of minicamp following offseason knee surgery but was very hands-on with Sweed throughout the weekend, as he was in the past with Plaxico Burress and current teammate Santonio Holmes.
"Those guys brought me in,'' Ward said. "Unfortunately, they left and I was the leader in Year 3, and it was me just learning on the run. But I remember vividly just coming into the league. In my time it was [looking up to] Kordell [Stewart] and Jerome, now these guys, they see Ben [Roethlisberger] and Troy [Polamalu] and they're in awe.''
Mendenhall, 20, is in awe mostly because he never thought he would become a Steeler. He didn't visit Pittsburgh during the entire draft process, and the team all but ruled out landing the Big Ten Player of the Year with the No. 23 overall pick.
Mendenhall was a projected top-15 selection. But on draft day he fell behind Oregon's Jonathan Stewart (No. 13 to Carolina) and former Arkansas tailbacks Darren McFadden (No. 4 to Oakland) and Felix Jones (No. 22 to Dallas), paving the way for the surprise scenario.
"I didn't think I would be the fourth running back taken, but everything happens for a reason,'' Mendenhall said.
Both tailbacks have taken different paths to the NFL.
Parker entered the league through the back door as an undrafted free agent after receiving little playing time at the University of North Carolina. Mendenhall received the red-carpet treatment last weekend as the team's first-round pick. He held his own news conference and received Pittsburgh's No. 1 jersey, which annually goes to the team's top selection.
Despite differing pedigrees, together the two could form one of the best one-two punches in the league next season.
Their collective talents were on display during minicamp.
With darting runs throughout the weekend, Parker also showed he hasn't lost any speed following his return from last year's broken fibula. He was leading the NFL in rushing with 1,316 yards before his leg injury in December.
On Mendenhall's first day of practice, he caught a short pass on a check down from Roethlisberger. He then quickly changed direction to elude a would-be defender and sprinted up the field for a long gain.
You could hear several "oohs" from onlookers after that play. Unfortunately, Pittsburgh didn't see much more of Mendenhall after he tweaked his hamstring and was held out for the remainder of minicamp. His hard luck continued this week when he reportedly was robbed at gunpoint early Monday near his hometown of Chicago. No one was hurt in the incident.
Once the season starts, the Steelers expect Mendenhall to improve their flexibility on offense as well as the durability of Parker, who had 658 carries the past two seasons.
Steelers offensive coordinator Bruce Arians is in the process of devising schemes to use both players in the same backfield. It's a package that has Parker and Mendenhall excited for next season, when the pair could give opposing defenses nightmares as dual running and receiving threats.
"It can be real dangerous,'' Parker said. "Defenses won't know what we can do. Usually when I'm in there, defenses would always try to put a bracket on me and try not to let me get down the field. With [Mendenhall] in there, it will open it up.''
Parker is seeing the positives of adding Mendenhall, and that can be nothing but good news for the Steelers and their rookie first-round pick.
One of the most memorable things Bettis told Parker in his rookie season was that he should always push the veteran as hard as he could, Parker said. That way, Bettis remained sharp as the starter, and Parker in turn became a better running back. Years later, that same advice is being passed down to Mendenhall.
"I was kind of nervous coming in, but that running back room with Willie, it's been nothing but professional since I've been here,'' Mendenhall said. "They're trying to help me as much as they can. The better I do, the better they're going to do as a team.''
Memo to Bettis: "Fast Willie" is keeping his promise.
James Walker covers the NFL for ESPN.com