The authority say they will draw up contingency plans over the next few months, and aims to have a set of policies in place for October.
The deputy leader of the council, Michael Payne, said if Government ministers are preparing for the scenario, then the council should too.
He said it would be irresponsible for the council not to prepare and it should look at what the impacts would be of several scenarios, including getting a trade deal with the EU, or ending up with no trade deal.
The UK is set to leave the European Union on Friday, March 29 next year.
The latest move by Gedling Borough Council comes after the Government revealed it was making preparations to ensure an adequate supply of food and medicines if Britain left without a deal.
Theresa May said people should take “reassurance and comfort” from these preparations.
Today (August 2) Councillor Payne, who represents the Redhill ward for Labour, said: “There are concerns that we saw expressed by the foreign secretary yesterday about the Government leading us accidentally towards a no-deal Brexit.
“There is clearly some need for us now to start doing some work about what the contingency plans are for us in Gedling if there’s a no deal Brexit, or if we’re heading towards a hard Brexit.
“If the most senior Secretaries of State are expressing concern about it, and they’re overseeing the process, then we certainly ought to be doing some work.
“I think we need to pull together some officers this week and start modelling what the impact is.
“We’ve got a responsibility for economic development, and for our town centres, and business that will be impacted in the borough.”
A report is now expected to come back to the council before the end of the year.
Council leader Cllr John Clarke, who represents the Netherfield ward for Labour, said: “People are going to stockpile this and stockpile that, and it’s not just about paracetamol, we represent 117,000 people and the logistics of doing that are sometimes quite complicated.
“Once that panic button is pressed, and that’s what I think might happen, shelves will get cleared, you see it with Christmas, for that one day off at Christmas people go out and panic buy.”