The Royals have been given permission to speak with the 20-year-old England Under 21 international after agreeing an undisclosed fee with The Robins.
"It's an exciting prospect because Reading are ambitious to make the Premiership and that is where I want to be," he told the clubs official website.
"It's more about playing Championship football than money as far as I'm concerned.
"It's up to me now that an offer has been accepted. It's not an easy decision and I won't make the move if I don't think it's right.
"I'll have no problem staying where I am. I've had four years at Ashton Gate and have been very happy."