The LUCIFER project aims at deploying the first array of enriched scintillating bolometers for the investigation of neutrinoless double-beta decay of Formula: see textSe. The matrix which embeds the source is an array of ZnSe crystals, where enriched Formula: see textSe 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 textSe 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 textTh, Formula: see textU and Formula: see textU are respectively: Formula: see text61, Formula: see text110 and Formula: see text74 Formula: see textBq/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 textSe allowed us to establish the most stringent lower limits on the half-lives of the double-beta decay of Formula: see textSe to 0Formula: see text, 2Formula: see text and 2Formula: see text excited states of Formula: see textKr of 3.4Formula: see text10Formula: see text, 1.3Formula: see text10Formula: see text and 1.0Formula: see text10Formula: see text y, respectively, with a 90 % C.L.