We use the manifestly Lorentz covariant canonical formalism to evaluate eig
envalues of the area operator, acting on Wilson lines. To this end we modif
y the standard definition of the loop states to make it applicable to the p
resent case of noncommutative connections. The area operator is diagonalize
d by using the usual shift ambiguity in the definition of the connection. T
he eigenvalues are then expressed through quadratic Casimir operators. No d
ependence on the Immirzi parameter appears.