Generally speaking they use two types of fabric: 1) textile (natural) lining 2) synthetic lining.
Examples of synthetic fabrics include the following: polyester, acetate, acrylic, ozone, nylon, viscose, rayon, spandex, kevla, lastex, and orlon. Scientists have exclaimed that when they examine synthetic fabrics under a microscope they look like plastic threads that are 'spun' or 'weaved' together. Adidas rarely print which synthetic fabric they use in their inner linings - when printing online feature lists for their shoes - but the likely candidates are either: polyester, viscose, or nylon.
Examples of textile (natural) fabrics include the following: cotton, silk, linen, paper, and wool. Wool is typically an insulating fabrics that is rarely used in footwear - more commonly socks. Cotton and linen, on the other hand, are comfortable and 'breathable' natural fabrics that are the likely candidates that Adidas uses for their textile inner lining. Alongside being comfortable and breathable, these fabrics are also: absorbent, soft, durable, crease easily, and they can also be washed by hand.