Rotherham boss Ronnie Moore said: "Jason has gone out on loan to get some games under his belt.
"He hasn't featured much this season, Rochdale came in for him and we feel that it is a good deal for both parties."
Leicester have sacked Claudio Ranieri as they face up to a relegation battle just nine months after their stunning Premier League title.
Leicester's euphoria at winning the league last season has evaporated, with Claudio Ranieri leaving the club.
Manchester United are on the longest run without a penalty of any Premier League club, in contrast to their historical reputation.
The latest gossip and rumours from the newspapers and online:WAYNE ROONEY'S agent is in China in a bid to arrange
The latest gossip and rumours from the newspapers and online:WAYNE ROONEY is ready to quit Manchester United and take up