The Millers, who have already made seven signings this summer, will face games with Morton, Livingston and Ayr over the next five days and are in discussions with a young striker over a move to the New York Stadium, rumoured to be Morecambe's Jack Redshaw.
Assistant boss Paul Raynor is keen to get a deal done in time for him to be involved in Scotland.
"We are taking 23 players up there and things are ongoing about getting one more in," Raynor said after Saturday's opening pre-season win against Parkgate FC.
"We will hopefully have 24 players up there and it is a chance for everyone to show what they can do in the games."
The Millers return home for a run of four home friendlies against Bolton, Huddersfield, Middlesbrough and Barnsley.