Wrap, which has up to £4m of grants left in its £8m Innovation Fund, said it believed there were opportunities for slashing the amount of materials used to make boxes for breakfast cereals, frozen foods, laundry detergents, multipacks and sanitary products.
Applications are open to any company on the condition the innovation will have a clear route to market.
In a previous project paid for by the Innovation Fund, Wrap worked with Iceland on a trial to cut packaging for frozen pizza by as much as half. Wrap grants made in the past have ranged from £10,000 to £650,000.
Tendering is open until 11 December with applicants shortlisted by 20 December and projects set to start as early as next February.
Up to 2.14 million tonnes of paper packaging may be entering the UK household waste stream every year, according to Wrap.