Warner's agent said he has offered a two-year deal worth $23 million, with $12 million guaranteed.

"We had a lot of talk today and we conveyed what it means for Kurt to stay in Arizona," agent Mark Bartelstein said Tuesday night.

The Cardinals reportedly offered a two-year, $20 million contract with $10 million guaranteed. Warner had sought a deal that would rank with the top five paid quarterbacks in the league: two years for some $29 million.

Bartelstein said Warner's counteroffer is "clearly below what his market value is out there and the Cardinals know that."

Warner's counteroffer came a day after he made a highly publicized trip to San Francisco for an interview and physical exam with the 49ers. Warner and his wife Brenda were flown from Phoenix by a private jet and taken to 49ers headquarters by limousine.

But with San Francisco expected to have a run-oriented attack, Warner seemed an unlikely fit. All along, he has made it clear he wants to stay in Arizona, where he has two of the NFL's top wide receivers in Larry Fitzgerald and Anquan Boldin.

Bartelstein sounded optimistic about the chances of reaching an agreement. He said the offer to Arizona was much less than what Warner could have gotten from San Francisco.

"If we were to do a deal with the 49ers it would be substantially more," Bartelstein said.

Cardinals general manager Rod Graves did not return a message left on his cell phone.

He has said repeatedly the team wants Warner back but that a deal would have to fit in with the organization's other personnel plans. Warner's value undoubtedly is affected by the fact he will be 38 before next season begins.

The Arizona Republic said the team was preparing a counteroffer of its own Tuesday night, with the possible sticking point the amount of money guaranteed.

Warner was the heart and soul of a prolific passing offense that led Arizona to an unexpected run to the Super Bowl. The Cardinals had playoff victories over Atlanta, Carolina and Philadelphia before a thrilling 27-23 loss to Pittsburgh in Tampa. Warner completed 31 of 43 passes for 377 yards and three touchdowns against the Steelers.

In four playoff games, Warner completed 68 percent of his passes for 1,147 yards and 11 touchdowns, with three interceptions. That was after he completed 67 percent of his throws in the regular season for 4,583 yards and 30 touchdowns, with 14 interceptions.