Maxted, who came through the youth system at Doncaster was released last summer after joining Walsall on trial rather than sign a new deal at the Keepmoat.
He spent the second half of last season with League Two side Hartlepool United, where he failed to make an appearance before being released in the summer.
The 21-year-old was drafted in by non-league side Forest Green Rovers last midweek for their pre-season friendly with Championship side Cardiff City.
He did his cause of a move to Rangers no harm, according to reports, with a man of the match performance for Rovers that included a penalty save from Peter Whittingham.
Should McCarthy move it will leave only Robert Green and academy prospect Joe Lumley as men between the Rangers sticks.