Tottenham and Everton are both said to be watching over the young defender.
The report claims that a number of Premier League sides have been tracking his progress over the summer.
Ralston has been on international duty with Scotland’s under-21’s, as he featured in a 2-0 win over Holland this week.
The 18-year-old defender has played seven times for the Celtic first-team, making four appearances so far this season.
He was given the chance to impress in pre-season and is highly thought of at the club.
The defender has already begun training with the senior Scottish national side, with Gordan Strachan seeing him as one for the future.