Rotherham manager Ronnie Moore is keen to turn on-loan midfielder Mark Randall's deal into a permanent one.
The 21-year-old joined the Millers in October, but has only played 20 minutes after suffering a broken collarbone in his debut at Southend.
He has returned to full training and will battle for a place in Moore's side over the New Year fixtures, with the Millers boss already impressed by Randall.
"We'd like to have him here," Moore said. "It depends what Arsenal want to do and what he wants to do.
"His loan deal is up on January 25 and hopefully he will have three or four games in by then so he'll get to know us and we'll get to know him.
"He's a fantastic player and our fans will love him."