The versatile left wing-back, 20, was among the heroes in France last Saturday when victory over Mexico in the final gave England Under-21s a third successive Toulon Tournament title.
Rams boss Lampard and his assistant Jody Morris watched Dasilva in action in the Young Lions' semi-final win over Scotland.
Also in action then were Stamford Bridge 20-year-olds Jake Clarke Salter and Fikayo Tomori as well as Chelsea midfielder Billy Gilmour, 17, who played for the Scots.
Charlton are keen to take Dasilva back after he lifted the club's Player of the Year award at the end of a season-long loan. But at least two Premier League clubs and a handful of Championship outfits want him to continue the next phase of his development with them.