"I think it's important that you let a player get away for a while and see what that feeling is when you're away from the game for a month, two months and see if that feeling changes," Girardi said. "Because it's hard to come back once you leave when you're an older player.
"I would just say to Mo, 'Think about it, and make sure. Just make sure that's exactly what you want to do. And if that's what you want to do, I respect it. As good as you've been, I still think you can probably do it.'"
Asked about Girardi's comments after the game, Rivera said, "I don't know why we're talking about this again."
The 43-year-old has been on something of a farewell tour this season, meeting employees and fans of other teams at road ballparks and receiving gifts from opposing teams.
"I don't tell anyone what to think or don't think. I respect that," Rivera said. "But again, I made my decision."
Girardi said he wants to talk to Rivera about it because, when he was a player, he never wanted to think, "Could I have played more?"
Girardi wasn't able to stay healthy over the final years of his career, but Rivera has shown very little wear and tear this season despite tearing his ACL last year.
The Yankees closer is 4-2 with a 2.12 ERA this year, and he recorded his 40th save of the season on Tuesday, marking the ninth time the all-time saves leader has reached the 40-save plateau.
For his career, Rivera has converted 648 saves in 726 chances and compiled a 2.21 ERA.
Girardi said he still believes Rivera will retire at the end of the season, but he wants to talk to him during the offseason just to make sure.
"It's a man who retired talking to another man who's thinking about retiring and just telling him my feelings on it," Girardi said. "It's not me lobbying for him to come back, because as I've said all along, I would never want a player to come back if he didn't want to come back.
"I think he can still do the job."