Spurs are without Harry Kane until the end of the season as he is out with a hamstring tear.
Piatek would be as suitable replacement for Giroud, who will likely complete a move to Inter in the coming days.
Piatek’s future at Milan is in doubt following the signing of Zlatan Ibrahimovic, who has scored on his debut for the club.
Despite scoring consistency for Milan last season after joining from Genoa, where he burst onto the scene, the goals have dried up this term.