Denmark was in the business of selling of her Indian and African colonies due to being unable to sustain them 1830-1850 (mostly to Britain). The capital of Lithuania is Vilnius, an inland city. What on earth would the Danes do with a landlocked enclave surrounded by Russian (and perhaps a bit Prussian) territory?
Denmark, since 1814, had no interest in the Baltic beyond her own provinces. Rather the status of Schleswig and Holstein and the conflict with Austria and Prussia over that issue was Denmark's foremost concerns.