Cashman characterized Teixeira's recovery from a strained left calf injury as "slow."
"I don't think he's close to getting back here," Cashman said during an interview with Sirius XM radio Tuesday morning. "I think we'll have a chance to get him back before the season's over ... maybe the Toronto series on the road, which is a little ways down the line here in that last week of the season."
Cashman said the team hopes Teixeira gets healthy before the playoffs, assuming the Yankees qualify. New York (83-63) is currently a half-game ahead of the Baltimore Orioles (83-64) for first place in the American League East Division.
Teixeira has been out since re-injuring his left calf while trying to beat out a double-play grounder on Sept. 8 in Baltimore.
The Yankees have missed his switch-hitting power bat in their lineup. Teixeira, 32, is batting .255 with 23 home runs and 81 RBIs in 120 games this season.
Cashman also said that left fielder Brett Gardner could be activated from the disabled list as early as Tuesday to serve in a pinch-running and defensive role. He will not be able to hit, though.
Gardner has been out since April 18, when he injured his right elbow, and was forced to undergo surgery as a result.
Mike Mazzeo is a regular contributor to ESPNNewYork.com.