The England Under-21 international has begun the campaign in sparkling form and scored a hat-trick against Wolves last weekend.
That made it seven goals in five league games for the youngster, who spent last term on loan in the Championship with Aston Villa.
Abraham has been with Chelsea since Under-8 level, and worked his way through the ranks to their senior team.
And Drogba, who scored 164 goals for the Blues, believes that the 21-year-old may have taken inspiration from him during his time at the club.
“I've known him since he's been like this," Drogba told Sky Sports.
"These are kids we used to see, they used to come and watch us training, and I believe they learned a little bit of our skills, how we read the game.
"So, you know, we're not surprised because I also trained with them when I used to train with the reserve team.
"It was always a moment for me to give away some skills, some knowledge, and they learned really fast, really quick.
"So once again, I'm not surprised with what I've seen.”
Abraham is one of several youngsters to be given a chance in the first team under Frank Lampard, along with the likes of Mason Mount and Fikayo Tomori.
Drogba has been encouraged by the work of his former team-mate since he took over in the summer.
"I think he is focusing on Chelsea and it happens that he needs to work on young players, to give them a chance,” said the Ivorian.
“Being an ex-player from the club, it helps a lot because we've seen all these kids when we were training.
"So you have to give them a chance and when you do, they deliver.
"They've been performing. Of course, there will be maybe a lack of experience in big games like the Champions League but I'm not worried.
"I'm really happy with the work that Frank is doing right now. And the fans, and the people who know football, they understand."
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