The Sun says the 33-year-old striker is keen to move to the Far East after a string of lucrative offers in recent weeks.
He has been promised £200,000-a-week deals by Dalian Aerbin and Shanghai Shenhua.
Now Chinese champions Guangzhou Evergrande have joined the chase and are ready to top any offer from their Super League rivals.
Ivory Coast international Drogba is down to the last six months of his Stamford Bridge contract and has rejected their offer of a one-year extension.
Nicolas Anelka has already secured a move to Shanghai next month.