The three-year, $2.55-million offer to Kilger, the fourth pick overall at the NHL draft in July, is $150,000 more than the contract signed by No. 3 pick Aki-Petteri Berg of the Kings.
However, the limit of $850,000 a season applies only to salary and signing bonuses, leaving performance bonuses as the final points to be resolved.
Kilger must be signed by midnight Thursday to play in the NHL this season, but both sides have expressed confidence they will reach a deal. Larry Kelly, Kilger's agent, has said "it would be silly for both sides not to."
Kilger came to camp without a contract but made it imperative for the Ducks to sign him by becoming their top center, scoring four goals and 10 points in eight exhibition games. The Ducks, who had said they wouldn't raise their $766,000-a-year offer, responded by meeting Kelly's counter of $850,000.
Though Kelly has said he isn't "asking for the moon" in bonuses, General Manager Jack Ferreira characterized them as "high" and countered Monday with bonuses similar to those given to players in the past.
"Now it's up to him," Ferreira said. "We'll see what happens."