Lloris was signed by Andre Villas-Boas from Lyon for £12.3 million in the summer but, despite the Frenchman's fee and impressive reputation, the manager has opted to keep Brad Friedel as first choice so far this season.
And Coupet feels that his compatriot may need to move away in order to save his talents from being wasted on the bench, highlighting the presence of four first-team keepers at Spurs.
|11/1||Tottenham are 11/1 with William Hill to win the Europa League
Coupet also played for Lyon, winning the Ligue 1 title seven times with the French giants, and expressed his bemusement at how training sessions can work with Friedel, Lloris, Heurelho Gomes and Carlo Cudicini to choose from.
He continued: "There are four keepers. I don’t understand how things go in training. It is a terrible waste of time for him there."
Lloris was given a rare start in a 3-1 Spurs win over Maribor in the Europa League on Thursday evening, but made a mistake to concede a goal which may well see Friedel return against Manchester City on Sunday afternoon.
However, Coupet doesn't believe the goal was Lloris' fault, instead blaming Kyle Naughton for playing a risky back pass to the keeper: "[The goal] was provoked by a team-mate. The pass-back was disastrous. It was not down to a lack of confidence. His qualities are there and the fact his team won changes things."