The scheme in Baker Street by East Yorkshire joint venture firm Marblechip has secured outline planning permission from city councillors.
Director Paul Dixon said the decision meant talks with a potential call centre client could continue with the aim of bringing more than 100 new jobs to the development.
He said negotiations with a potential occupier for part of the proposed 42,000sq ft office space available at the development were ongoing.
“We are still in talks with a potential call centre occupier," he said.
“We are in competition with other sites, including one on the South Bank, but with outline permission we now have something on the table and can also offer a tailor-made solution to whatever requirements they might have in terms of use of space within the building.”
Subject to a further detailed design approval, the four-storey complex will be built on a site currently occupied by a former motor garage.
Council planning officers had recommended refusal for the office project, claiming it would put the development of other key city centre sites earmarked for future office use at risk.
But Mr Dixon said: “There is nothing of this size and at this price in the city centre office market at the moment.
“In this recession everyone is looking at their costs and we believe we can offer competitive rates at Baker Street.”
See today's Business section in the Mail for more on this story.