Five teams are seeking approval to bid a third link, estimated at $500 million, of an $8.7-billion rail line now under way between New Jersey and Manhattan.

The contract, to be awarded next fall by project owners New Jersey Transit and the Port Authority of New York and New Jersey, will involve building 14,600 feet of soft-ground tunnels that run 110 feet under the Hudson River. The project is set to be the nation’s largest public works transit job.

There are some new names on the list of firms seeking contract prequalification that had not bid the project’s previous two hard-rock tunneling segments on either side of the river. Those contracts were awarded recently.

Set to vie for the under-river contract are: a joint venture of J.F. Shea Construction, Schiavone Construction Co. and Kenny Construction; a team of S.A. Healy, China Construction America and Halmar; a JV of Spain’s FCC Construction, Austria’s Beton and Monierbau and U.S.-based Ferreira Construction; a team of Spain’s OHL and Tully Construction; and a team of Skanska USA, Traylor Bros. and France’s VINCI.

A team comprised of Schiavone, Skanska and Shea was awarded a $271 million contract for the New Jersey tunneling segment earlier this month. A joint venture of Barnard Construction Co. and Judlau Contracting won a $583-million award for the Manhattan tunneling in December. Project owners will complete the Hudson segment prequalification review in March, says a New Jersey Transit spokesman.