The deal is for one year, according to a source briefed on the negotiations.
The sides have hammered out the rough framework of a deal that would pay the 38-year-old approximately $16 million, about $1 million more than he made in 2013. But talks continue on other details, the source said.
Although he appeared to tire down the stretch, going 0-6 with a 6.56 ERA in his final eight starts, Kuroda finished the season 11-13 with a 3.31 ERA, the lowest among Yankees starters who qualified for the ERA title, and he topped 200 innings for the third straight season.
Last month, Kuroda declined a $14.1 million qualifying offer from New York.
Kuroda's potential deal was earlier reported by CBSSports.com.
Also Friday, the Yankees finalized a $3 million, one-year contract with utilityman Kelly Johnson. The 31-year-old is an eight-year big league veteran and hit .235 (86-for-366) with 16 homers and 52 RBIs this year for Tampa Bay.
Johnson played third base this past season for the first time in his big league career, making 12 starts, and could see time there next season. Alex Rodriguez's status is uncertain as he contests his 211-game drug suspension.
When the deals for Ellsbury and Kuroda are finalized, the Yankees will have committed about $157 million to 12 players for their 2014 payroll.
That would leave them approximately $20 million to spend if they intend to stay under the $189 million luxury-tax threshold, which includes all players on the 40-man roster and $11 million to $12 million for benefits.
It appears unlikely New York would stay under the threshold unless Rodriguez is suspended for most of the season, which would relieve the Yankees of much of his $25 million salary.
Information from The Associated Press was used in this report.