The Germany international only moved to West Ham last summer from Borussia Dortmund, but has had an injury-plagued start to his Premier League career.
IlBianconero says Juve are eyeing Fullkrug and are keen to setup a loan arrangement with the Irons.
Juve see Fullkrug as cover for Dusan Vlahovic and would use him as a pinch hitter when the Serb needs resting.
For his part, Fullkrug may be left unconvinced by the prospect should Juve firm up their interest.