Bounty hunting is a crime in Mexico.
Chapman and his two co-stars on the show "Dog The Bounty Hunter," were arrested and jailed in Hawaii last week.
The U.S. Attorney's Office has until Oct. 16 to file papers in support of their extradition, but Chapman's attorney, Brook Hart, hopes to resolve the issue before then.
Chapman said he would offer an apology, pay a fine, forfeit the bail he posted in Mexico and make a charitable contribution, Hart said.
"What he's prepared to do is take responsibility for not having to stay around to face the charge," he said.
The trio had ensnared convicted rapist Andrew Luster, the Max Factor heir, on June 18, 2003, in Puerto Vallarta, Mexico. But they, too, were arrested by Mexican authorities.
Chapman posted about $1,300 for his release, and based on "flawed legal advice" thought he could leave the country and Mexican authorities would have no further interest in him, Hart said.
Chapman's capture of Luster, who had fled the country during his trial on charges he raped three women, catapulted the 53-year-old bounty hunter to fame and led to the reality series on A&E. Luster is now serving a 124-year prison term.