Single-photon sources represent a key enabling technology in quantum optics, and single color centers in diamond are a promising platform to serve this purpose, due to their high quantum efficiency and photostability at room temperature. The widely studied nitrogen-vacancy (NV) centers are characterized by several limitations, thus other defects have recently been considered, with a specific focus of centers emitting in the near-infra red (NIR). In the present work, we report on the coupling of native NIR-emitting centers in high-quality single-crystal diamond with solid immersion lens (SIL) structures fabricated by focused ion beam (FIB) lithography. The reported improvements in terms of light collection efficiency make the proposed system an ideal platform for the development of single-photon emitters with appealing photophysical and spectral properties.