Express Sport understands that the Motherwell midfielder is unimpressed with the offer that the champions have made.
The door has not been closed on the move, but there will need to be a significant shift from the Parkhead club’s side to get the deal over the line.
The concern for Turnbull is that he fears, with the offer on the table, that he isn’t being viewed as a regular first-team player.
Celtic know the wage that Turnbull is currently on at Motherwell and, although there has been a significant increase, the feeling is it is not in line with a player who is set to play a big part under Hoops boss Neil Lennon next season.
The Celts are ready to hand Motherwell a club record fee but are notorious for offering lower wages when they take players in from other Scottish clubs.
Turnbull and his representatives don’t feel they are being unfair or have tabled unfair demands. The 19-year-old, who scored 15 league goals last season, knows there is strong interest in him from England.
Barnsley have already failed with a bid, while Bristol City have also inquired. Premier League Southampton and several other English clubs, including Brighton, are continuing to monitor the situation.
Turnbull knows there is enough interest there and is confident that, even if he doesn’t move in this window, that his stock will continue to grow if he maintains the form of last season, which saw him win the Scottish Football Writers’ Association young player of the year award.