This trio are set to officially return to their respective parent-clubs at the end of May.
Edmonds-Green was signed on a season-long loan deal from Huddersfield Town last year and went on to make 28 appearances for Rotherham in the third-tier as they sealed automatic promotion on the final day of the campaign.
Osei-Tutu joined the Millers in the January transfer window following a injury-hit spell with Nottingham Forest in the Championship.
As for Grigg, the forward managed to show some signs of promise for Rotherham after joining the club on loan from Sunderland.
Before suffering a season-ending hamstring injury, Grigg managed to provide eight direct goal contributions in all competitions.
Making reference to his aforementioned trio, Warne has revealed that he is open to bringing them back to the AESSEAL New York Stadium when the transfer window opens next month.
Speaking to the Yorkshire Post, Warne said: “I liked all my loan signings.
“I loved Griggy, Jordi and ‘REG’.
“He got (briefly) injured and we only got Jordi match-fit right at the end and Griggy flying until he got injured.
“I would like to keep all three if I possibly could or consider it.
“In fairness to Jordi, he is an Arsenal player and it is about what they want to do, not what I want to do.
“Especially with REG, he is a very ‘Rotherhamesque’ player.
“But respectfully, Huddersfield might have him in their plans next year.
“They wanted him to play games and he has played no end and has done really well.”
When you consider that Grigg, Osei-Tutu and Edmonds-Green all played a role in the club’s promotion-winning campaign, it is hardly a surprise that Warne is keen to sign them again.
According to Rotherham Advertiser reporter Paul Davis, Grigg has already been offered a deal by the Millers and thus he could potentially join the club if Sunderland allow his contract at the Stadium of Light to expire.
As for Edmonds-Green, his future may depend on whether Huddersfield secure a return to the top-flight via the play-offs as he is unlikely to feature at the highest level next season.
Arsenal may also be willing to send Osei-Tutu out on loan again if Rotherham are able to provide them with assurances regarding game-time as the full-back needs to be featuring regularly in order to make strides in terms of his development.