The company currently has two sites in York and one each in Chester, Shrewsbury and Salisbury, and is looking to secure further locations across the UK.
A spokesperson says the group has seen high levels of demand for its roast dinner-inspired menu and will likely launch the funding drive in the next few months.
It comes after York Roast Co recently completed a refurbishment of its York, Shrewsbury and Chester restaurants, with Salisbury also set for a redesign.
The family-run business, founded by father and son duo Wayne and Stephen Chadwick in 2004, hopes the investment campaign will help it reach the ‘next level’.
York Roast Co’s menu includes its Yorkshire pudding wraps filled with meat, vegetables, stuffing, gravy and sauce.
It recently launched its first sweet option, with chocolate, brownies, Oreos and a Flake wrapped inside a giant Yorkshire pudding.