Dailly, 34, returned to West Ham this week after spending two months on loan with the Championship club.
Saints have been beset by defensive injuries this season with Claus Lundekvam and Darren Powell still out.
"I've had a good chat with him. He knows that I think a lot of him, and we'll take it from there in January," Burley told BBC Radio Solent. "It was a big disappointment when Christian left."