Coppinger, one of Doncaster's highest earners, was allowed to leave the League One club on the final day of the summer transfer window to be reunited with former Rovers manager Sean O'Driscoll at Nottingham Forest.
However, the 31-year-old midfielder has struggled for opportunities at Forest, starting only one Championship match and making three other substitute appearances.
And Saunders has left the door open for Coppinger to remain at the Keepmoat Stadium when he comes back to Rovers in the new year.
"James understands that they are paying all of his wages and that we had to let him go, but what happens next depends on what Nottingham Forest want to do," Saunders said. "He's only started one game for them in two months. He has been on the bench for most of that time, which is frustrating for him and for us.
"We have just got to wait and see how it develops, that is why I've signed players until January. He has got another year left on his contract here so he is still very much our player and the door is open for him."