Grigg joined the Millers on loan in August and has scored two goals in 13 appearances since the move.
There were fears in South Yorkshire that Sunderland could recall Grigg after Rotherham striker Freddie Ladapo handed in a transfer request last week.
The Black Cats are level on points with Rotherham at the top of League One, with both sides well placed in the battle for automatic promotion.
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Yet Grigg, who joined Sunderland in 2019, will be out of contract at the Stadium of Light this summer and is unlikely to be handed another chance on Wearside.
EFL rules also state that Sunderland wouldn’t be able to sell or loan Grigg to another club this season because he has already appeared for two clubs – after coming off the bench for the Black Cats’ Carabao Cup tie at Port Vale.
Warne has held talks with Sunderland boss Lee Johnson about the situation.
"I spoke to Lee this week at length," Warne told the Rotherham Advertiser. "He reassured me there is no issue with Griggy. I wouldn't expect him to go back on that.
"I trust Sunderland and I trust their manager, so I don't foresee a problem."
As for Ladapo, who has scored eight times in 21 League One appearances this campaign, Warne says there have been no offers for the 28-year-old frontman.
Sunderland were linked with the striker over the weekend, yet Rotherham wouldn’t sell on the cheap.
Ladapo’s contract is set to expire this summer but the Millers have a one-year extension option.
"There's no interest that I know of," said Warne when asked about Ladapo following his side’s FA Cup penalty-shoot-out defeat at QPR.
"However, I could turn my phone on in about ten minutes and I might have someone telling me that something's happened."
Sunderland will have the chance to move ahead of Rotherham in the table when they host Lincoln on Tuesday.
The Millers will now travel to Fleetwood in League One this weekend.