Sloan Gibson will meet with local Veterans Affairs Department officials and construction managers Thursday.
The half-finished hospital is expected to cost up to $1.73 billion, nearly three times the estimates given last year. Gibson and others have blamed problems in the contract process and an excessive design.
The VA has asked Congress for an additional $600 million to finish, but some lawmakers are balking. They want the VA to fire those responsible for the overruns and make significant changes in the way it plans and builds hospitals.
Construction has continued under a series of short-term agreements while a long-term funding deal is negotiated to finish the work.