The 16-year-old has recently been on trial with the Scottish Championship side.
Knox has previously enjoyed trials with a host of Premier League sides, including Tottenham, Manchester United and Liverpool, but it appears that he is set to complete a move to Ibrox after the board gave the green light for a £100,000 switch (via The Scottish Sun).
The Scottish Sun adds that the youngster is keen on joining the Light Blues due to the fact that Mark Warburton has proved that he is not afraid to turn to those shining in the development sides if an opportunity in the first-team arises since he arrived in the summer.
If the Scottish Championship winners do manage to get a deal across the line, it will be the latest boost from what has been a hugely positive spell for the club.
The side booked their place in the top flight for next season after wrapping up the title with a 1-0 win over Dumbarton on Tuesday, and have the Challenge Cup final and Scottish Cup semi-final both ahead, so could be returning to the Premiership with a domestic treble and the signature of one of the most exciting prospects in the game.