Per Wojnarowski, a Cavaliers source said, "[Rose is] tired of being hurt, and it's taking a toll on him mentally."
K.C. Johnson of the Chicago Tribune reported those close to Rose aren't sure what he'll do.
Cavaliers head coach Tyronn Lue said he does expect Rose back, though there's no timetable, and he added that the team members "all have his back" as he goes through a "personal matter," per team play-by-play announcer Fred McLeod.
Nick DePaula of ESPN noted that if Rose retired outright, he'd leave the remaining six years and $70 million of his Adidas shoe deal on the table.
Rose has appeared in seven games this season and is averaging 14.3 points, 2.6 rebounds and 1.7 assists per contest while shooting 47.0 percent from the field.
He experienced some major highs, including winning the 2010-11 NBA MVP award after averaging 25.0 points, 7.7 assists and 4.1 rebounds per game.
Rose also dealt with some significant lows with multiple knee injuries, which cost him all of 2012-13 and all but 10 games in 2013-14.
While Rose put up 18.0 points per game with the Knicks last season, representing his best production since 2011-12, injuries continue to hamper him.
He has been effective as a starter when healthy this season, but when Isaiah Thomas returns to action from a hip injury, Rose figures to be relegated to a bench role should he decide to continue his career.