Courteney Cox Offered $1 Mil to Promote Cougar Hunt

10/13/2010 9:00 AM PDT

Courteney Cox Offered $1 Mil to Promote Cougar Hunt

She's barely a single woman ... but Courteney Cox is already getting a $1 million offer to become the new face of a dating website ... one that specializes in hooking cougars up with fresh meat.

TMZ has learned ... just one day after it was announced that Courteney separated from David Arquette, -- a website that specializes in matching older women with younger men -- mailed her a $1 million contract to become their official spokes-cougar.

We're told CL believes Courteney's personal "circumstances" -- coupled with the fact that she stars in "Cougar Town" -- make her the perfect candidate.

As far as the contract goes -- Cox would be required to voice 12 radio ads, appear in 4 TV ads, and make at least 30 public appearances for the CL brand ... all within the span of one year.

But there's a catch -- CL would reserve the right to fire Cox if she gets arrested or "conducts herself in a manner that brings herself into disrepute."

So far no word on whether CC plans to sign.