The young midfielder has been on trial with the Foxes and played some reserve team football.
Manager Nigel Pearson told the club website: "He's a strong lad and has a desire to learn.
"We've given him an opportunity and will continue to monitor his progress within the first team environment."
Pearson added: "It's early days for him yet but he has impressed me so far."
Verma is eligible for a place in Saturday's League One clash against Carlisle United.