The Sun says Shanghai Shenhua say they have an agreement to sign the 34-year-old, who has left Chelsea on a free. But United Arab Emirates side Al Wasl, managed by Maradona, hope to persuade him to join them.
They can match the £300,000-a-week wages the Chinese are willing to pay Drogba.
And they hope that big donations to his charity will help their cause.
Maradona said: “Who in the world would not want Drogba? Every team would love to have such a player in their ranks.”