Southampton are said to be willing to make a move for the full-back in the summer.
However, Deila is hoping that Tierney’s head won’t be turned by the speculation over his future, as he predicts that many more clubs will announce their interest before the next transfer window.
"I can tell you they won't be the last club coming up here to see him," said Deila.
"When you have an 18-year-old playing for Scotland and regularly for Celtic then, of course, clubs are going to be after him.
"But he's going to stay here because it's the best thing for his development.
"I've had a long chat with him about what's best for his development and now he just has to concentrate on being consistent for us.”
Tierney has enjoyed a wonderful breakthrough season at Parkhead this season, where he has featured in 25 matches.
The 18-year-old has not looked overawed with any challenge thrown at him, and he has shown his class in both European and domestic action.
Tierney only recently signed a new four-year deal at Celtic, but that has seemingly not put Premier League clubs off.
If Tierney did complete a move to Southampton, he would join the likes of Victor Wanyama and Virgil Van Dijk in making a switch from Parkhead to St. Mary’s in recent times.