The speedy winger has really caught the eye over the last couple of months and is attracting positive comment in the media, who have suggested he could be used as a 'wild card' entry into this England's World Cup squad.
Martin's concern is purely domestic and says Aaron's current ambitions should be simply about improvement and treading the road towards realising his potential.
"Every match he plays he will gain experience," commented the Head Coach. "I think he can become more influential and we tell him that because at the age of 19 you can improve in every game.
"To play for a club like Tottenham at White Hart Lane at that age, you want to improve and he wants to do that.
"We need that with all the young players, if they don't improve and develop, we will be a normal club - and we want to be an exciting club."
Martin Jol believes Aaron Lennon can become more influential with each passing game.