We discuss the construction of the exactly solvable pairing models for bosons in the framework of the Quantum Inverse Scattering method. It is stressed that this class of models naturally appears in the quasiclassical limit of the algebraic Bethe ansatz transfer matrix. We propose the new pairing Hamiltonians for bosons, depending on the additional parameters. It is pointed out that the new class of the pairing models can be obtained from the fundamental transfer-matrix. The possible new application of the pairing models for confined bosons in the physics of helium nanodroplets is pointed out.