Chief executive Rick Parry is thought to have met Kraft on Monday.
The talks related to either chairman David Moores diluting his major shareholding or naming rights for Liverpool's proposed new stadium.
No formal proposal has been made, but talks are expected to continue.
The European champions are still hoping to build a new stadium in Stanley Park, but costs are believed to have risen significantly from an initial estimate of £70million.
The Kraft Group bought gridiron side New England Patriots for £98million in 1994 and also own Major League Soccer team New England Revolution.
Moores is not thought to be looking to relinquish his entire 51 per cent shareholding, according to BBC Sport.
