He joined Middlesbrough last July from Manchester City, having spent loan periods at Lincoln City, Bournemouth and Blackpool.
Rogers, an England Under-20 international, has made 33 appearances this season in all competitions, scoring seven goals including a consolation goal in Middlesbrough's 6-1 League Cup semi-final second leg defeat to Chelsea at Stamford Bridge.
Aston Villa, fifth in the Premier League standings, are away to Sheffield United on Saturday.