Dillon, who set an NFL single-game record by rushing for 278 yards last season, wants to see what kind of offers he gets in free agency, agent David Levine said.
The Bengals can automatically keep Dillon for one more season by using its transition tag on him and matching any offer. General manager Mike Brown has said repeatedly and emphatically that he will do so.
The Bengals have plenty of room under the salary cap to match an offer for Dillon.
"Why would you not tag him? He realizes he's going to be a transition player," Levine said. "That does not mean they're going to match whatever offer they get."
Brown wasn't available for comment at home Wednesday night but reaffirmed on the team's Web site that he will use the transition tag on the running back.
Dillon, 25, set a club record by rushing for 1,435 yards last season, fifth-highest in the NFL. He became the eighth player in league history to rush for 1,000 yards in each of his first four seasons.
Although Dillon likes the run-oriented offensive philosophy of coach Dick LeBeau, he also wants to play for a winner. The Bengals have gone 4-12 each of the last two seasons and haven't had a winning season since 1990.
Brown has refused to discuss the team's offer to Dillon. Levine said it included a $12 million signing bonus and base salaries would bring his total for the first three years to $19.5 million.
The base salaries would increase each year after the third year, making the total package worth $60 million over eight years, Levine said.
Dillon wanted a bigger signing bonus and wanted to see what kind of offers he'd get from other teams, Levine said.
"I think anybody would think it's a good offer," he said. "Obviously he thinks he's going to get more money in free agency."
Levine can begin talking to other teams when free agency begins March 2. The Bengals would have to extend a one-year contract offer for about $4 million in order to protect their rights to match any offer from another team.
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