That’s according to German newspaper Hamburger Morgenpost who say the Premier League champions were vying for his signature.
Arp was in contract limbo at the Bundesliga side - and Chelsea were ready to take full advantage.
However, the 17-year-old spurred their advances to pen fresh terms with the club.
Hamburg legend Horst Hrubesch thinks Arp is a future star.
He told Hamburger Morgenpost: ”The boy has something.
"No, actually he has everything! I believe he can pave the way for HSV. "
Chelsea had a frustrating summer in the transfer market although Antonio Conte did splash the cash.
Alvaro Morata, Antonio Rudiger, Tiemoue Bakayoko and Danny Drinkwater were all big-name arrivals.
However, Conte as had a lengthy list of targets he failed to sign.
The Italian wanted Romelu Lukaku - but the Belgian bruiser opted to join Manchester United.
A fee was agreed for Alex Oxlade-Chamberlain only for the midfielder to quit Arsenal for Liverpool instead.
Meanwhile Ross Barkley decided mid-Blues medical that he didn’t fancy Stamford Bridge after all.
Chelsea will face Leicester at the King Power Stadium on Saturday.