The club have yet to make a concerted strike in the summer transfer window, although they have completed one piece of incoming business with the addition of former Sheffield United keeper Josh Chapman on Wednesday afternoon.
The 18-year-old - recently released by the Blades - has been brought in to initially feature in the club's development squad while providing back-up to Viktor Johansson and Josh Vickers.
Chapman, who had been on trial, has signed a one-year deal with a further 12-month option.
Meanwhile, Warne - currently with the Millers squad on a summer training camp in Budapest - has revealed that a deal has been agreed with an unnamed player to become the club's first major close-season signing, pending a successful medical, with hopefully more to come.
The Millers chief said: "I think I have got one in the building. It is just in regards to his medical which is going to be later this week and the start of next week, so I don't really want to announce that and will keep that under wraps until everything is done.
"I am pretty close on a midfielder and have improved a bid on a defender, who I obviously won't name and on another player. It is a utility payer, so I have made an offer on that.
"I am hoping that some of those will fall into place when we come back from Budapest.
"I am really hopeful that by the end of next week that we should have three or four new faces in. But it has been going on this long that, until you get them in the building, you just never know."
On the outgoing front, Matt Crooks continues to be the focus of much transfer speculation with Ipswich having seen several bids turned down and several other clubs monitoring developments.
Striker Michael Smith has also been linked with several clubs including Bristol City, Middlesbrough and Millwall.
Warne added: "There has been interest and a lot of noise at the start of the off-season on both players. I think it has calmed down on one of the players.
"There is still a real interest in Crooksy and I am always worried when someone is calling me and I don't know the number. I don't know if it someone phoning for Smudge (Smith), (Ben) Wiles or (David) Barlaser or (Freddie) Ladapo. You just don't know.
"But at the moment, Crooksy is still our player. I always said that I still expect one or two outgoings. Not that I want (it), but I would be a liar if I didn't say I expected it."