Dillon's agent, David Levine, said the offer was too low.
Dillon was the eighth NFL player to rush for 1,000 yards in each of his first four seasons. He finished this season with 1,435 yards on 315 attempts, both team records and career highs.
"It's every guy's dream to have his best season the season before he is eligible for free agency," Levine said. "For him not to test the free-agent market, it's going to have to be an extraordinary offer."
Dillon, who set a single-game rushing record with 278 yards Oct. 22, reportedly is asking for $5 million-$7 million a season with a $10 million signing bonus, according to Thursday's Cincinnati Enquirer.
The amount of the Bengals' initial offer was not released.
The Bengals have the right to match any offer if, by March 1, they make him a one-year offer of about $4 million. That amount is estimated to be the average of the top 10 salaried NFL running backs.
The team plans to match any offer made to Dillon if it can't sign him before free agency begins.
"If we can't sign Corey, we will reserve sufficient cap room to meet what someone else might do," owner and president Mike Brown said. "We're trying to sign Corey Dillon."
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