Rose agreed to the lifetime ban in August 1989 following an investigation for Major League Baseball by outside lawyer John Dowd that concluded the career hits leader bet on the Reds to win while managing the team. Rose applied for reinstatement in September 1997 and met in November 2002 with Commissioner Bud Selig, who never ruled on the application.
Rob Manfred succeeded Selig in January.
Manfred said after meeting with the Los Angeles Dodgers in spring training on Monday that he has a formal request from Rose.
"What I intend to do is be in communication with his representatives, and we'll talk about how we'll handle it from a process perspective," he said.
At the time of the Rose investigation, Manfred was an associate at Morgan, Lewis & Bockius, a law firm that worked on labour law matters for MLB. He was not involved in the investigation.
"I want to make sure I understand all of the details in the Dowd Report and Commissioner Bart Giamatti's decision," Manfred said. "I want to hear what Pete has to say, and I'll make a decision."
Rose, who turns 74 next month, denied for 15 years that he bet on baseball. In his 2004 autobiography, "Pete Rose: My Prison Without Bars," he reversed his stand and acknowledged he bet on the Reds while managing the team.
These days, Rose spends time is Las Vegas signing baseballs for money. That may not fit the lifestyle then Commissioner A. Bartlett Giamatti suggested when the ban agreement was announced.
"The burden is entirely on Mr. Rose to reconfigure his life in a way he deems appropriate," Giamatti said at the time the suspension was announced.
The Hall of Fame's board of directors voted in 1991 to bar anyone on the permanently ineligible list from the Baseball Writers' Association of America ballot. Since his last year of BBWAA ballot eligibility would have been 2006, the impact of reinstatement on his Hall chances is not clear.