Mirrors made of silicon have been proposed for use in future cryogenic gravitational-wave detectors, which will be significantly more sensitive than current room-temperature detectors. These mirrors are planned to have diameters of ≈ 50 cm and a mass of ≈ 200 kg. While single-crystalline float-zone silicon meets the requirements of low optical absorption and low mechanical loss, the production of this type of material is restricted to sizes much smaller than required. Here we present studies of silicon produced by directional solidification. This material can be grown as quasi-monocrystalline ingots in sizes larger than currently required. We present measurements of a low room-temperature and cryogenic mechanical loss comparable with float-zone silicon. While the optical absorption of our test sample is significantly higher than required, the low mechanical loss motivates research into further absorption reduction in the future. While it is unclear if material pure enough for the transmissive detector input mirrors can be achieved, an absorption level suitable for the highly reflective coated end mirrors seems realistic. Together with the potential to produce samples much larger than ≈ 50 cm, this material may be of great benefit for realizing silicon-based gravitational-wave detectors.