Yankees general manager Brian Cashman was to make the offer to Sabathia's agents, Greg Genske and Scott Parker, either on Friday or in the next few days, the official said.
New York, whose streak of 13 consecutive playoff appearances ended, also plans to make offers to pitchers A.J. Burnett and Derek Lowe, the official said.
Cashman and Genske did not return telephone calls seeking comment.
Sabathia went a combined 17-10 for Cleveland and Milwaukee this year after winning the 2007 AL Cy Young Award, and is considered the best starting pitcher in this year's free-agent class.
Other top free-agent starters are likely will wait for Sabathia to set the price for pitchers.
"The signing of CC is going to create probably a truer market for a number of the pitchers, mainly because the clubs that are bidding on CC didn't get him, and the demand for the other pitchers will be greater," said agent Scott Boras, who represents free agents Oliver Perez and Lowe.
The 171 players who filed for free agency after the World Series could start negotiating money with all teams starting at 12:01 a.m.
EST Friday. Boras, based in California, said his phone was ringing repeatedly late Thursday night.
"I got eight phone calls. They didn't wait till the business day. You're talking about owners, your talking about general managers, people taking very aggressive stances with particular players," said Boras, who also represents outfielder Manny Ramirez and first baseman Mark Teixeira, among the top free-agent sluggers.
"They wanted to make sure they were on the board making offers," Boras said.
Francisco Rodriguez tops the available relief pitchers, a group that also includes Brian Fuentes and Kerry Wood. Agent Paul Kinzer said he had received inquiries from four teams about K-Rod, who saved a record 62 games for the Los Angeles Angels.
"I just think we've got to be patient. We'll know when the fit's right," Kinzer said. "When we get closer, we'll probably meet with the people, maybe check out the area, living arrangements, that type thing, and then make a decision."
He also reported an aggressive market for another client, shortstop Rafael Furcal.
"There's been about five or six serious teams already on him today, and I expect that to even go up because there's been at least eight or more that have been in contact," Kinzer said.
Commissioner Bud Selig repeatedly cautions teams to be careful in their spending, but the economic downtown doesn't appear likely to depress salaries for top players.
"We think that the time of free agents will still be recession-proof," said Lew Wolff, owner of the low-revenue Oakland Athletics. "We think the second tier will present some opportunities."
Other high-profile free agents include pitchers Ryan Dempster and Trevor Hoffman; first baseman Jason Giambi; outfielders Garret Anderson, Bobby Abreu, Milton Bradley, Pat Burrell, Adam Dunn and Ken Griffey Jr.; catchers Jason Varitek and Ivan Rodriguez; and third baseman Casey Blake.
"A lot of the owners want to sit down and have a meeting with some of the players," Boras said. "There's a couple players in this market that pay for themselves, in Teixeira and Ramirez, and they know that."
It's rare that a player spends his entire career with one team.
Wood wanted to stay with the Cubs, who instead acquired Kevin Gregg as a less costly alternative.
"It will be tough sitting on the other side," Wood said.
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