The Boron neutron capture therapy is one of the promising methods for treating a number of oncological diseases. The essence of the method is the accumulation of a large content of boron by diseased cells, localisation of these cells, and their subsequent irradiation with thermal neutrons. Boron-containing nanoparticles are the main components of boron delivery systems to cancer cells. However, the boron fluorescence region is in the 400-500 nm range, which complicates further localisation of cancer cells since the transparency region of human tissues is in the 750-1000 nm range. This problem can be solved using nanoshells consisting of a dielectric core and a metal shell. The authors demonstrate that these nanoshells can be designed to produce a strong absorption that gives rise to a plasmon resonance in the near-infrared wavelength region. This feature, based on Fano resonance phenomenon, allows invoking such nanoshells for fluorescence enhancement of boron-containing nanoparticles to be used as markers in tumour cells. The closed-form expression for asymmetric resonance in a nanoshell is derived in the dipoleapproximation.