Coach Vincenzo Montella will make a late decision on the 25-year-old Colombian, who picked up the problem during Saturday's 2-1 Serie A defeat against Inter Milan.
A statement from La Viola read: "Cuadrado will receive specific treatment over the next two days and then be assessed before Thursday's Europa League tie against Esbjerg."
Montella will also be hoping to recover midfielder Juan Manuel Vargas in time for the trip to Denmark.
Vargas fractured a metacarpal at the weekend and underwent surgery on Monday.
The Peruvian will wear a protective brace when he returns to the pitch.
One player who will miss the midweek encounter is Argentinian centre-back Gonzalo Rodriguez, who suffered a thigh strain against Inter and will undergo further tests.