The LUCIFER project aims at deploying the first array of enriched scintillating bolometers for the investigation of neutrinoless double-beta decay of [Formula: see text]Se. The matrix which embeds the source is an array of ZnSe crystals, where enriched [Formula: see text]Se is used as decay isotope. The radiopurity of the initial components employed for manufacturing crystals, that can be operated as bolometers, is crucial for achieving a null background level in the region of interest for double-beta decay investigations. In this work, we evaluated the radioactive content in 2.5 kg of 96.3 % enriched [Formula: see text]Se metal, measured with a high-purity germanium detector at the Gran Sasso deep underground laboratory. The limits on internal contaminations of primordial decay chain elements of [Formula: see text]Th, [Formula: see text]U and [Formula: see text]U are respectively: [Formula: see text]61, [Formula: see text]110 and [Formula: see text]74 [Formula: see text]Bq/kg at 90 % C.L. The extremely low-background conditions in which the measurement was carried out and the high radiopurity of the [Formula: see text]Se allowed us to establish the most stringent lower limits on the half-lives of the double-beta decay of [Formula: see text]Se to 0[Formula: see text], 2[Formula: see text] and 2[Formula: see text] excited states of [Formula: see text]Kr of 3.4[Formula: see text]10[Formula: see text], 1.3[Formula: see text]10[Formula: see text] and 1.0[Formula: see text]10[Formula: see text] y, respectively, with a 90 % C.L.