The high street giant announced last week that it will be wound down after rescue efforts failed.
It will continue to trade through its 124 UK stores – including its shop in Scarborough’s Brunswick Shopping Centre – to clear stock while seeking offers for all or parts of the business.
After that, if no alternative offers have been received, all stores will shut.
Yesterday, it was revealed that Mike Ashley’s Frasers Group was in talks over a potential deal for the retailer.
Scarborough Council’s Conservatives have now raised concerns that the closure could impact on the authority’s bid for £10 million in government funding from the Future High Streets Fund.
Cllr Heather Phillips, the group’s deputy leader, said her party’s councillors had not been given a say on the Town Centre Strategy.
Cllr Phillips said: “Our main concern is the Town Centre bid and how it could be affected by the closure of Debenhams.
“The Town Centre Strategy initiated under the previous administration was the result of a fantastic team working with residents, business owners and elected members.
“The new Labour-Independent administration took over with an emphasis on ‘openness and transparency’.
“However, this did not extend to the promised role on the board put together to plan for the implementation of the strategy.
“As the largest group on the council we had been promised a say, this didn’t materialise. A few planters on Aberdeen Walk and Vernon Road to cover up seagull mess don’t enhance the offer to residents and visitors.”
Cllr Phillips added: “We do have a small number of independent traders who show we can offer a mixed retail experience but we need to offer more.
"If the Debenhams site becomes vacant it may not attract a major retailer, what is the plan B from our Town Hall?
“I await a response to my request for an urgent briefing and update. It is needed to show Scarborough Borough Council has the ability to adapt the strategy and manage the change for our residents benefit”.
In response, the council’s cabinet member for Inclusive Growth, Cllr Liz Colling, said that the council’s concern was with those who would be losing their jobs.
She said: “We will use our established jobs task force to offer support to local staff to do what we can to help find them alternative employment.
“The stores will continue to trade for the time being and be open as usual in the run up to Christmas We will also work with the Brunswick Centre to attract new tenants if the existing operators cannot be saved.
“Our town centre strategy recognised that we need more than just a retail offer
“To respond to the wider issue of changing High streets our town centre strategy team are developing plans for how we can move towards a mixed use environment.
“Our £10 million application to the government’s Future High Street Fund was submitted in July and we hope to receive an update before the end of the year.
“Separately, we have also submitted our Town Investment Plans for both Whitby and Scarborough, as part of the Town Deals for these two towns.
"The Town Deal board for Scarborough included both local conservative MPs who are fully supportive of these plans.”
Cllr Colling said that the council had carried out “extensive public engagement as well as briefings for elected members”as part of the process.