Work will cover the construction and maintenance of a 23km stretch from junction 25 to 28 in the east Midlands.
Up to five bidders will be invited to tender for the deal. Firms have until the end of November to express an interest.
A Costain and Mowlem joint venture bagged a £430 million deal to upgrade a stretch of the M1 motorway in southern England in September.
Alfred McAlpine, Mowlem, Nuttall, Costain, Birse and Balfour Beatty are understood to have prequalified for an initial £20 million scheme to widen the motorway between junctions 31 and 32, close to Sheffield.