The work will cost £1.5 million and is intended to help safeguard the historic symbol of Black Country industry for future generations.
Work will be carried out to restore the structure, which is already one of the best preserved of the UK's surviving glass cones, and it will also see weeds removed from the Wordsley landmark, built between 1788 and 1794.
Councillor Simon Phipps, Dudley Council's cabinet member for regeneration and enterprise, said plans for the repair work are progressing and an application for scheduled monument consent had been submitted but will need to be approved before any work can take place.
Plans are now being finalised, with an expectation that work will start next spring.
Councillor Phipps said: “I’m pleased that plans to repair the cone are progressing.
"Surveys have now been completed and we have submitted an application for scheduled monument consent, which is necessary to obtain before any works are allowed to proceed on such a historic building.
“We’re currently finalising the work programme in readiness for repairs to start in the spring and we look forward to the day we can reopen the cone to visitors.
“Although the cone is currently closed, the rest of the site is open to the public and visitors are very welcome to browse the on-site store, visit our fantastic collection of independent stores and dine in the café.”
Announcing the scheme earlier this year, he said: "We’re very lucky to have such a well-preserved historic monument in our local area, which ties into hundreds of years of history.
"It would be remiss of the council not to make the absolute most of such a wonderfully historic building, which is why we’re putting in £1.5 million to restore the structure, and keep the Red House Glass Cone educating and entertaining people from all over for another hundred years."