The town's new Conservative MP said such a centre would be "vital" to coordinate the response to flooding from bodies including the Environment Agency and the borough council.
Ms Clarke made the call in a behind-closed-doors meeting with Staffordshire MPs and county council chiefs on Friday, during which she also demanded that Shire Hall is reopened "as soon as possible".
Stafford, along with other parts of the Midlands, has been badly hit by flooding due to weeks of storms and heavy rainfall, leading to increased water levels along both the River Sow and Penk.
Ms Clarke said "a lot more could be done" to deal with the flooding, and that "not enough joined up work" was taking place between the agencies involved.
"I want to see a flood control centre here in Stafford, like they have in some other constituencies, which can coordinate with all of the different services," she told the Express & Star.
"This model has run very effectively in other parts of the country. For residents to be looked after, and to make sure they are getting the help that they need, there needs to be very clear lines of communication among the agencies concerned.
"Given the scale of the storms that we have had, and my belief that weather is only going to become more extreme due to climate change, a flood control centre is vital."
The dire weather conditions last week forced two town centre car parks to close. Heavy rainfall continued over the weekend.
Meanwhile, Ms Clarke, who succeeded Jeremy Lefroy as Stafford MP in December, has also vowed to make the reopening of Shire Hall a priority.
The 18th century pile in Market Square closed more than two-and-a-half years ago under controversial circumstances, and has since been used sparingly for one-off events.
Council chiefs unveiled new plans for it last year, including a £7 million scheme featuring space for small business start ups, a restaurant or bar and an exhibition space.
Since then progress on the Grade II listed landmark appears to have stalled.
Ms Clarke revealed she has raised the issue with Stafford Borough Council with a view to getting the hall reopened to the public.
"It is such an important asset right in the heart of the town, and getting it reopened and brought back into public use as soon as possible is a real priority for me," she said.
"There are lots of different ideas around what the best uses for Shire Hall are."
Ms Clarke added that she is planning to chair a meeting in the coming weeks with stakeholders to discuss the best options for the site's future.
See Thursday's Express & Star for a full interview with Theo Clarke MP.