The City reserve goalkeeper was set to join the League Two club last week after the Millers first choice stopper Andy Warrington was injured. The deal was all set to go through until Johnson discovered that he would not be able to recall Basso in the event of Adriano Basso or Stephen Henderson being injured.
Johnson has called on the FA to review their rules for short term loan deals in a bid to prevent such hindrances to clubs having to dip into the market in due to an emergency.
He told the Bristol Evening Post,
"I spoke to Mark Robins (Rotherham manager) and he was happy for Chris to go there and get some games while their regular keeper, Andy Warrington, was out injured."
"It's a ridiculous situation that doesn't seem to benefit anyone."