Lampard rejected the American club last summer but has a two-year deal. on the table, says the Daily Star.
The Major League Soccer outfit are willing to pay the England midfielder £72,000 a week to follow in the footsteps of David Beckham.
Lampard is having almost a replica season to last year - with Chelsea making no attempt yet to open talks about a new deal.
They waited until mid-May until giving him a one-year extension.
But this season the midfielder has found himself with stiff competition for a place in the Blues' starting line-up.
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