Grigg is on a season-long loan from Sunderland this term, but will play no further part after he had to go under the knife on a hamstring injury.
The 30-year-old will be a free agent in the summer as the Black Cats will release him and Warne wants to keep him in South Yorkshire.
“I’ll definitely speak to him,” Warne said. “Just because he’s injured now doesn’t mean there’s a long-term problem. He’ll come back from it. It’s not like he’s 38 or something.
“I really like Griggy. Whatever league we’re in, I think the club should try to keep him.
“He ‘gets’ the club, he gets what we’re about. He’s great to coach and manage and has become an integral part of the dressing room.
“I like to have four strikers and I’d like to think he’ll be one of them.
“Unfortunately, his season is over. He’s going to have a repair which will leave him out for longer.
“The surgeon and our medical team think that will give him the best chance to make the best recovery.”
The Millers are back in action when they host Morecambe on Tuesday, hoping to take another step towards League One promotion.
Along with Grigg, Rarmani Edmonds-Green will also miss out with a hamstring injury.
First-team coach Matt Hamshaw said: “"It will be tough, first and foremost.
"I think you've only got to look at their results - although I know they're having a little bit of a bad run at the minute.
"We've got huge respect for Stephen Robinson and the players they've got. Cole Stockton has been a massive threat for them, Diagouraga has had a good career and a lot goes through him.
"We ended up winning 1-0 up there but it was tough. A wind-assisted goal by Smudge did it.
"There's been a lot of teams played them and struggled against them and they do like to play football."