The Mirror reports that the MLS side are keen to bring in Drogba as David Beckham is set for a move to Paris St Germain when his contract expires next month.
LA Galaxy face competition from Russian giants Anzhi, who are also keen on signing the 33-year-old striker.
Drogba is keen to sign a new contract with Chelsea, but has so far failed to agree terms with the Blues.
Italian giants AC Milan are also keeping tabs on Drogba’s situation at Stamford Bridge.
