He has left the Black Cats at the end of his contract and will be available on a free transfer.
Warne has spoken openly about his desire to bring Grigg back to South Yorkshire on a permanent contract and will now kick-off negotiations.
“I’m going to have a conversation with his agent,” Warne said.
“I would like to keep Griggy but it’s down to the player. He’ll consider the geography of it, the finances of it, what other offers he gets.
“It might be something we sort out in a couple of weeks, it might be something we revisit in July.”
Grigg’s injury - a torn hamstring - in February coincided with Rotherham’s toughest spell of the season as they missed his link-up play with Michael Smith.
“It was a massive loss for us when he got injured,” Warne said.
“A striker’s job isn’t just to score. Look at Smudge, he’s been brilliant for us over the years but it’s only this season that he’s scored 20-plus goals.
“Griggy was the glue in our team. When he was injured his boots weren’t easy ones to fill.”