Hanks (Lucky Guy) will compete against Lane (The Nance) for the Outstanding Actor prize, while Vanessa Redgrave (The Revisionist) is in the running for the Outstanding Actress title, as is Up in the Air's Amy Morton (Edward Albee's Who's Afraid of Virginia Woolf?).
Other stand-out nominees include Midler (I'll Eat You Last: A Chat with Sue Mengers), who will fight against Ugly Betty star Michael Urie (Buyer & Cellar) for Outstanding Solo Performance, and actor-turned-bluegrass musician Steve Martin (As You Like It), who is mentioned in the category of Outstanding Music in a Play.
The 58th annual Drama Desk Awards, which celebrate the best in New York theatre, look set to be a big night for Off-Broadway production Giant and short-lived Broadway musical Hands on a Hardbody - both are up for nine trophies.
The accolades will be presented during a ceremony at The Town Hall in New York City on 19 May (13).