The 34-year-old striker left Chelsea in the summer on a free transfer, but reports of financial trouble at the Chinese club has led to rumours that he could return to the Premier League.
But Drogba says that he will see out his current deal for the Chinese Super League outfit, and believes he has no incentive to go elsewhere.
"I hope more because I'm really happy here. I miss the Premier League because it's the best league in the world, but really I don't regret my choice," he told BBC Sport.
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"I just arrived like two months ago so I'm really happy. I am, I'm really happy here so I have no reasons to leave. I don't want to leave here."
Drogba scored 157 goals in his eight years at Chelsea and scored the decisive penalty in their Champions League triumph over Bayern Munich at the end of last season.
The Ivorian has since scored five goals in seven games for Shenhua, who he joined midway through their campaign, and hopes to win trophies with the club in the future.
"I want to stay here, as long as I can win some trophies with my team and make our fans very happy," added Drogba.
"It's difficult at the moment, but I know that there's hope and I believe."
Drogba says he will "never forget" his time at Chelsea, and the moment they lifted the Champions League trophy, describing it as the "best moment of my career".
"To be able to win it in that kind of game was perfect and it's something you will never forget," he said.
"But you have to carry on in life, so now I am focused on what I can bring to the Chinese league.
"Hopefully, within a few years, when my contract finishes here, I will be sitting with you and talking about how fantastic it was to win the Asian Champions League."