A league source told the NFL Network that Jones' representative, Ray Savage, had several conversations with the Bengals during the cornerback's visit, and the sides have the nucleus of a multiyear deal in place.
Savage and the Bengals expect to put the contract to paper this week, according to the NFL Network, and Jones should join the team's offseason program Monday.
Jones' agent, Tom Hunter, told The Associated Press the Bengals hadn't made a formal contract proposal as of Tuesday evening. Jones was in town for his second workout with the team this offseason.
Cincinnati is among a handful of teams that showed an interest in Jones, who was released by the Dallas Cowboys after the 2008 season and didn't play last year. Only 26 years old, Jones has seen his career bottom out because of his repeated arrests.
He was suspended for the entire 2007 season and for six games with the Cowboys in 2008 for violating the NFL's conduct policy.
The club had no comment on Jones' tryout Tuesday.
Jones went to West Virginia along with late Bengals receiver Chris Henry. The two of them got into so much trouble with their teams -- Jones was drafted in the first round by the Tennessee Titans in 2005 -- that commissioner Roger Goodell toughened the league's disciplinary policies.
The Bengals released Henry in 2008 following his fifth arrest. Owner Mike Brown referred to himself as a "redeemer" and did an about-face, bringing Henry back against the wishes of coach Marvin Lewis. Henry died in a fall from a pickup truck driven by his fiancee last year.
The Bengals became more cautious about signing troubled players after they had 10 arrested during a 14-month span. Henry and linebacker Odell Thurman were the main offenders, drawing repeated suspensions beginning in 2005.
The team has softened its stance in the last two years, bringing in players on low-risk deals. Running back Cedric Benson was released by the Chicago Bears after two alcohol-related arrests -- the cases were dropped after grand juries declined to indict -- and the Bengals signed him to a minimal financial deal during the 2008 season.
They took the same approach last season with running back Larry Johnson, who got a minimal contract and left as a free agent after the season.
In February, the Bengals signed receiver Matt Jones, who didn't play in the NFL last season, to a minimal one-year deal. Jones was charged with cocaine possession and with violating a plea agreement, prompting the Jaguars to release him after the 2008 season.
Pacman Jones has the longest history of off-field problems.
Tennessee drafted him expecting him to be a cornerstone of the defense for years. Instead, he was arrested six times and involved in 12 instances requiring police intervention. The Cowboys traded for him and he got into trouble again, drawing the six-game suspension for an alcohol-related scuffle with a team-provided bodyguard.
He appeared in nine game with Dallas, starting six, but failed to get an interception. He also returned punts and averaged only 4.5 yards, prompting the Cowboys to release him after the season.
The Bengals have one of the best cornerback tandems in the league in Johnathan Joseph and Leon Hall, who had six interceptions apiece last season. The defense finished fourth in the league, one of the main reasons Cincinnati won the AFC North with a 10-6 record.
Cincinnati drafted cornerback Brandon Ghee from Wake Forest in the third round last month, looking for depth at the position.
Information from The Associated Press was used in this report.