The former Blues forward has been the subject of speculation following reported financial trouble at the Chinese club, but insists he is happy with his choice to leave England.
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 rumors that he could return to the Premier League.
Drogba, though, 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," Drogba told BBC Sport. "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 its UEFA 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 its 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," Drogba added. "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 the Blues 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."