While the 31-year-old is said to be "happy" in Detroit and isn't looking for a move, such a decision wouldn't be in his control, reports Haynes.
The three-time All-Star has been one of the bright spots on a disappointing Pistons squad that currently sits outside of a playoff spot. The veteran guard is averaging 18.3 points and 5.9 assists across 37 appearances this season.
Rose inked a two-year, $15-million contract with Detroit in the summer.
Detroit could be heading toward a rebuild as the deadline approaches. Star forward Blake Griffin is out indefinitely with a knee injury while big man Andre Drummond has been the subject of trade talks.