The teenage right-back has been linked to Tottenham, Everton and West Ham in the past few weeks with stories about interest from south of the border regularly popping up in the press.
But the boyhood Hoops fan is under contract for another two seasons and the club are not thought to be concerned about his head being turned.
In fact, Ralston signed a three-year deal only last summer, with that improved contract coming only a year after he'd signed a two-year deal.
His wages will have been boosted on each occasion, yet he was clearly the lowest paid player on the pitch this week when he was asked to mark Neymar - the most expensive player in world football.
Celtic are in no hurry to reward Ralston just yet but are likely to hand him a new deal later in the season if he continues to hold down a regular first-team spot.