The 27-year-old made just six first-team appearances last season and has not featured for the beleaguered Black Cats since the EFL Cup defeat at Everton on September 20.
Rodwell, who has a year left on his contract, is understood to be keen on a move to the MLS, and Donald confirmed that a deal to end the player's time on Wearside early is said to be close.
"It's unlikely that Jack Rodwell will be here next week," Donald told the Roker Report podcast. "Him and his agent have been excellent to deal with.
"When players don't want to be here we need to be reasonable with them and they need to be reasonable with us.
"Jack Rodwell is being sensible, and if he's being sensible then there is a chance he will leave."
Rodwell has made 76 appearances for Sunderland - who will be playing in League One next season - since his 2014 move from Manchester City.