Emergency services were alerted to a possible sighting of a man falling into the River Kent at Staveley Road in Kendal at about 10:00 GMT.
Meanwhile, Pooley Bridge, on the B5320 near Penrith, has collapsed, according to reports.
There are currently 47 severe flood warnings in place for Kendal, Keswick, Cockermouth, Carlisle and Appleby.
The BBC is running a Local Live page providing updates on the weather and flooding.
Flooding started on Saturday as Storm Desmond brought more than a month's worth of rain in just 24 hours.
Cumbria Police declared it a major incident and said all emergency services were stretched.
Water is receding in many places although torrents of water are now reaching towns like Carlisle, downriver from the areas hit worst overnight.
The government's emergency Cobra committee met to oversee the deployment of troops and other resources in Cumbria to help people after the floods.
Environment Secretary Elizabeth Truss said the level of rainfall had been "unprecedented" and billions of pounds will be spent on improving flood defences.
About 4,000 homes are without power and Electricity North West will start planned outages for a further 5,000 at a time from 16:00 GMT to protect the overall supply to 60,000 homes after floodwaters hit a substation in Carlisle.
The planned outages are expected to last up to three hours.
Carlisle's hospital is running on a back-up generator and the trust that runs it, North Cumbria University Hospitals NHS Trust, has declared an internal major incident.
The West Coast main rail line north of Carlisle will remain closed for several days after 8ft of water flooded the railway.
The depth of the water, about two miles north of Carlisle station, has reached its peak but is not expected to clear until Tuesday.
About 200 homes were evacuated in Keswick after the water overwhelmed flood defences which had been built following major floods in 2009.
Mayor Paul Titley said: "We'd rather have a one-in-100-year flood every 100 years, not every six - we were a bit surprised to get another one so soon.
"I think the [flood defences] did work, but they were completely overwhelmed by the amount of rainwater we had.
"The river was 5.4m above ground - in 2009 it was 4.6m."
Water levels are now believed to have peaked across Cumbria with about 2,000 homes and premises expected to have been flooded.
The forecast for Sunday night is largely dry with patchy rain.
However there are yellow warnings for rain from about 17:00 on Monday until Tuesday morning.
A Met Office spokesman said: "Whilst this rain will neither be as heavy nor as prolonged as recent rain, please be aware that in view of the saturated nature of the ground and high river levels further localised flooding and disruption to transport is possible."

The Bears face must-win games in their final group matches in the T20 Blast and One-Day Cup to keep alive hopes of making the quarter-finals in both.
"There's no reason why it should be inconsistent, we know what we're meant to be doing," Brown, 46, told BBC WM.
"Under pressure, we're failing to deliver what we're supposed to."
Warwickshire's four-wicket defeat by Durham, who chased down 293 to win, leaves the third-placed Bears needing to beat current leaders Yorkshire on Monday to stay in the hunt for the last eight.
Before then, they go to Old Trafford on Friday knowing victory over Lancashire in their last T20 Blast game is vital to their chances of making the knockout stages.
Brown is confident the high-stakes nature of the next two matches will bring out the best in his side.
"We are a decent side - we're struggling a the moment as we're struggling to get the same team out on the park twice," Brown said.
"The guys who come in should be proficient at executing under pressure  - that's what we haven't done and that's what we need to do in these two games.
"We know we've got to win them and it's exciting to be part of."
All-rounder Keith Barker is set to return after injury at Old Trafford, while former England batsman Jonathan Trott could make a comeback against Yorkshire following a back problem.
Search teams are trying to find an elderly man thought to have fallen into floodwater in Cumbria.
[NEXT_CONCEPT]
Warwickshire director of cricket Dougie Brown admits he cannot explain why his side's white-ball cricket has been inconsistent this season.