Goal are among those claiming the 15-year-old will snub the likes of Barcelona, Bayern Munich, Manchester City and Manchester United to move to Stamford Bridge.
He will arrive for a fee of around £500,000 when his 16th birthday arrives in June.
"Billy is a talented player and I'm sure many clubs are looking at him," former Rangers boss Mark Warburton said over Christmas. "Big clubs have vast scouting networks covering that age group.
Read the full article on eurosport.co.uk: Chelsea 'win race' to sign Rangers wonderkid