And Posh manager Grant McCann is concerned he could lose the 17 year-old midfielder before the next transfer window closes on August 31.
Posh director of football Barry Fry told the Peterborough Telegraph that Chelsea, Arsenal and Spurs are among the clubs to have sent scouts to the ABAX Stadium this summer to run the rule over the precocious teenager.
McCann said: “Leo is a very good player and he’s been in very good form this summer so I hope I don’t lose him.
“There have been many clubs watching him and I’m not surprised. He’s strong, he’s athletic and he carries the ball very well.”
Da Silva Lopes has made just 10 appearances for Posh. He was spotted playing for Powerleague FC in local junior football.
Fry added: “The word is out that Leo is a very talented 17 year-old and clubs have been flocking to watch him.
“We have had no enquiries, never mind bids, but there have been an awful lot of scouts coming to our games just to watch him.
“Chelsea, Arsenal and Sours are among those to have sent scouts to watch him.”
Da Silva Lopes will play in Saturday’s (July 23) friendly against Leeds United at the ABAX Stadium when he could be joined by Leicester City left-back Callum Elder.
Fry is hopeful a deal to bring Elder back to the club on loan will be completed tomorrow (Friday).
The Posh management have also held discussions about signing a new striker after a poor start to the summer friendlies by the club’s forward players.