The agency expects the event to take place in early March for the initiatives, which are to be procured separately under a design-build-finance-maintain model.
Interested parties should submit contact details to Lesley Cole by midday on 26 January.
Earlier this week, Highways England awarded the contracts for financial advisory services on the projects to PwC.
Under current plans, works for the £1.3bn A303 project will involve the delivery of a 2.7km tunnel under the Stonehenge World Heritage Site, a bypass for Winterbourne Stoke and improvements to junctions between the A303 and the intersecting A345 and A360.
Works for the £1.5bn Lower Thames Crossing project involve a tunnel between the River Thames east of Gravesend and Tilbury, with new link roads to the M25 north of the river between junctions 29, 30 and to the A2 south of the river east of Gravesend.