Cashman said the two sides "mutually agreed to wait," after agent Matt Colleran called on Friday.
"It was a good conversation," Colleran said Friday evening. "By the end of it, we were on the same page."
Martin can become a free agent at the end of the season. Prior to agreeing on a one-year, $7.5 million deal before going to arbitration, Cashman had put forth the idea of a three-year contract that would have included this season.
On Thursday, Colleran told ESPNNewYork.com he planned to present Cashman a counter proposal that could serve to rip up this year's deal.
CBS Sports' Jon Heyman tweeted the Yankees were only prepared to go to three years and $20 million.
Martin will likely seek $8-10 million per year and will have more negotiating leverage if he has a good season. He was an All-Star last year but tailed off after the break.
Andrew Marchand covers the Yankees for ESPNNewYork.com.