The 20-year-old, who is a product of the Cottagers academy, has had 10 starts for the Imps so far and scored two goals, both against Hereford.
Manager Chris Sutton told BBC Lincolnshire: "I'm pleased Matthew is staying, but not so pleased he came off injured last night."
Saunders limped off late on during the draw with Dagenham & Redbridge.
Source: BBC Sport
Source: BBC Sport