The 35-year-old has been without a club since leaving the Black Cats.
Zenden have been close to joining both Nottingham Forest and Celtic in recent months.
Doncaster hope Zenden will join the likes of El Hadji-Diouf, Pascal Chimbonda and Marc-Antoine Fortune at the Keepmoat Stadium.
Doncaster’s club transfer advisor and agent Willie McKay told the Sunderland Echo: “We’ve spoken to Bolo. He played for Celtic in a friendly against St Johnstone.
“I’m a Celtic fan myself and I was told he was outstanding. But he couldn’t agree anything there and we’ve been in contact with him.”
“Sunderland offered me a new deal, but I didn’t sign because I wanted to move on,” Zenden said.
“Since then, I’ve been in contact with a few clubs and there have been a few offers. But they haven’t been what my mind was set on. I have been training six days a week and I am fit.”
