The 20-year-old, who has already been capped four times by Scotland, has been linked with a move to Spurs as well as several other Premier League clubs.
However, Mark Wotte, performance director at the Scottish Football Association, is concerned that a move could hamper the promising youngster's progress.
"The worst thing that can happen to him is that he could sign for an English Premier League club and not play. That could stop his development," Wotte told Sky Sports News.
"It's up to Jamie Forrest and his family, and up to Celtic whether they want to sell him or not."
Forrest has made 44 appearances for the Bhoys since his debut in 2009, scoring ten goals.