The London Evening Standard says they are hoping to convince Chelsea to let Anelka leave on a free transfer even though he has one year remaining on his contract.
Both MLS sides are interested in the striker, who is believed to be worried that he won't be a key part of Andre Villas-Boas's plans this season.
Anelka signed a one-year extension 12 months ago which increased his salary to £100,000 a week.
The former France international has been linked with a number of clubs in recent months but it is understood he would like to go to the MLS for a fresh challenge should the chance arrive.
However, they are hoping Chelsea realise that getting Anelka off the wage bill, saving them £5.2million, is an attractive proposition.