The Millers won automatic promotion to the Championship on the final day of the League One campaign.
Grigg is out of contract at the Stadium of Light this summer.
He is not expected to be offered a new deal by Sunderland and his time on Wearside has not gone to plan since a big-money move from Wigan Athletic.
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However, the striker has impressed during his loan spell with Rotherham boss Warne has spoken highly of the Northern Ireland international on several occasions.
Sunderland won their own promotion to the Championship over the weekend as the Wearsiders defeated Wycombe Wanderers in the League One play-off final at Wembley.
“I’m going to have a conversation with his agent,” Warne said via the Sheffield Star.
“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 tore his hamstring earlier in the season keeping him out for the majority of the campaign.
“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.”