The Ivory Coast defender signed for the north London side from French champions Paris Saint-Germain in a deal believed to be worth around £23m.
Aurier was linked with a host of English clubs before his move to Tottenham, with Manchester United thought to be among the contenders for his signature earlier in the summer.
However, Chelsea legend Drogba clearly feels that Aurier should have moved to Stamford Bridge ahead of White Hart Lane.
Blues icon Drogba told Sky Sports News on Monday: “I just spoke to him a few hours ago.
“He’s so happy to be in England and of course we’re going to help him.
“He’s my younger brother so I’m going to give him some tips: He plays for the wrong team! But I’m happy for him, very happy for his move.”
Chelsea got the better of Tottenham when the two sides met in the Premier League at Wembley last month as Antonio Conte’s men secured a 2-1 win over their London rivals.
The Blues, who won the title in Conte’s first campaign in charge last season, return to Premier League action on Sunday afternoon with a crunch clash against Arsenal at Stamford Bridge.
Tottenham, meanwhile, are preparing to host Swansea City at Wembley on Saturday as they look to pick up their first Premier League win of the season at the national stadium.
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