We show that if $f$ is a transcendental meromorphic function with a finite number of poles and $f$ has a cycle of Baker domains of period $p$, then there exist $C > 1$ and $r_0>0$ such that $\bigg\{z:\frac1C r\lt |z|\lt Cr\bigg\}\cap \mbox{sing} (f^{-p})\ne\varnothing,{\for}r\ge r_0.$ We also give examples to show that this result fails for transcendental meromorphic functions with infinitely many poles.