  We analyze an approximate interior transmission eigenvalue problem in
${\mathbb R}^d$ for $d=2$ or $d=3$, motivated by the transmission problem of a
transformation optics-based cloaking scheme and obtained by replacing the
refractive index with its first order approximation, which is an unbounded
function. We show the discreteness of transmission eigenvalues in the complex
plane. Moreover, using the radial symmetry we show the existence of (infinitely
many) complex transmission eigenvalues and prove that there exists a horizontal
strip in the complex plane around the real axis, that does not contain any
transmission eigenvalues.
