Yankees General Manager Brian Cashman, asked if he had an inkling that Cano — who left the team as a free agent after the 2013 season — might have been doping when he was with the Yankees, said he would have been heavily fined by Major League Baseball if he knew about it and kept quiet. M.L.B.’s constitution allows for fines of up to $2 million for failure to report such transgressions.

“If I have any knowledge of anybody past or present, I’m obligated to convey that knowledge to Major League Baseball,” Cashman said. “And I take that seriously, and so knowledge is one thing, suspicion is another.”

He added: “If we have knowledge of anything that’s basically cheating — drug abuse, what have you — if we choose to stay silent, we are jeopardizing our career in the game as well as significant fines.”

Though Cano, who left the Yankees as a free agent after the 2013 season, has few connections to the current Yankees, he has remained close with reliever Dellin Betances. The two spoke and texted earlier this week when Cano sustained a broken bone in his right hand after being hit by a pitch in Sunday’s game against the Detroit Tigers.

“As a close friend of mine, I really couldn’t believe it,” Betances said of Cano before the Yankees’ game on Tuesday in Washington.

Cano’s injury will not affect his suspension, which began Tuesday. Normally, players are paid while on the disabled list, but suspended players like Cano are not. He is in the fifth season of a 10-year, $240 million deal he signed with the Mariners in 2013.

Cano would be eligible to return Aug. 14, but he is ineligible for the postseason.

Entering Tuesday’s games, the Mariners were 23-17, a game and a half behind the Los Angeles Angels in the American League West. Seattle has not made the playoffs since 2001, the longest postseason drought in baseball.