If the two sides were to come to an agreement, it would make Martin a Yankee through 2014. Negotiations are in the early stages, however.
Martin, 29, is eligible to become a free agent after this season. He enjoys playing for the Yankees and is amenable to working within the club's financial goals. The Yankees want to get their payroll below $189 million in 2014, which under the new CBA would mean huge luxury tax savings.
"We would be flexible in their budget constraints," Colleran said Thursday.
If Martin were to have a strong year, he would likely be able to get a three-year contract on the open market. After last season, in which Martin made the All-Star team, his agent and the Yankees avoided arbitration by agreeing to a one-year contract for $7.5 million, with Martin able to collect another $25,000 to $100,000 based on reaching 400 to 475 plate appearances.
Colleran and Yankees general manager Brian Cashman last spoke Wednesday, and Colleran said he plans to present Cashman with his own proposal soon.
Cashman on Thursday night said that until he heard again from Colleran, he would not consider the two sides in negotiations.
"I would love to have Russell Martin stay," Cashman said.
Next offseason, St. Louis' Yadier Molina, along with Martin, could be the top free-agent catchers on the market.
Last year, Martin hit .237 with 18 home runs and 65 RBIs. Both manager Joe Girardi and Cashman were impressed with his defense, with Cashman even comparing Martin to Thurman Munson.
The Yankees have catching depth in their system even after trading Jesus Montero to Seattle for pitcher Michael Pineda. While there are concerns about Montero's defense, the Yankees planned to keep him at catcher. Still, the Yankees have backup Francisco Cervelli, along with prospects Austin Romine, Gary Sanchez and J.R. Murphy.
Andrew Marchand covers the Yankees for ESPNNewYork.com.