The full-back moved from PSG to Spurs on transfer deadline day for £23m.
That was after Tottenham sold Kyle Walker to Manchester City over the summer.
And Drogba is happy to see Aurier in the Premier League but wishes he had signed for Chelsea rather than their London rivals.
“I just spoke to him a few hours ago,” the Ivorian said to Sky Sports.
“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.”
Aurier has yet to make an appearance for Tottenham but he was on the bench for the 3-0 win over Everton at the weekend.
The France star could feature in the Champions League against Borussia Dortmund on Wednesday evening.
After that Tottenham return to top flight action when they host Swansea at Wembley.
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Chelsea made favourites to seal January deal for Premier League winner
Indeed, the Blues in our bar rate the Italian’s team highly after a fairly good start to the campaign, though don’t think there are enough bodies to deal with the constraints of Premier League and Champions League football.
So, the fact that Sky Bet make them favourites to land a Premier League winner in the January transfer market has gone down rather well today.
According to their transfer special on Leicester City star Riyad Mahrez, the English champions are just 5/1 to bring the Algerian to Stamford Bridge in the New Year.
Mahrez has previously been touted as a potential Chelsea target and is understood to have wanted to leave the Foxes in the summer, though ultimately remained at the King Power until January at least.
London rivals Arsenal come in at second favourites, though our resident Blues hope Mahrez can rediscover his best form and join Danny Drinkwater and N’Golo Kante at the Bridge.
The Algerian would be a wonderful addition for Chelsea. Though the likes of Eden Hazard, Willian and Pedro offer some degree of competition in attacking berths, Mahrez would add a whole added dimension and the idea of him feeding Alvaro Morata is a hugely exciting one.