The former Manchester United and West Bromwich Albion star plays with the Celtic left-back for the Scotland national football team.
Tierney is one of the best young players in Europe and has established himself as a key figure in the current Celtic team.
The 20-year-old can only get better in the coming years, especially working under former Liverpool and Swansea City manager Brendan Rodgers, who was appointed in his role as the Bhoys boss in the summer of 2016.
Fletcher, who is a veteran of the Premier League and won the league title five times, the Champions League once and the League Cup twice with United, has praised his Scotland international teammate Tierney.
The former West Brom star, who joined Premier League rivals Stoke in the summer transfer window, has also suggested that Tierney should remain at Celtic for now.
“He is a fantastic talent with a massive future,” Fletcher told The Glasgow Evening Times about Tierney. “I can’t speak highly enough of him either on or off the pitch. I think we are really witnessing the rise of a player who will be a very special talent.
“He will make his own mind up and make his own decisions,” added Fletcher about Tierney. “But right now he is playing Champions League football and he is part of something really special under Brendan Rodgers at Celtic who is a fantastic manager. There is plenty of time for him to go onto another level.
“The last thing you would want for him is to go and be another number somewhere – I am not saying that would be the case because I believe he will play at the very, very top level – but what I do know is that he will know himself when the time is right."