The weekend shows for the ITV reality show were cancelled and the celebrity contestants - who include 78-year-old ex-Strictly Come Dancing judge Dame Arlene Phillips and music producer Naughty Boy - were removed from the castle for their own safety following Storm Arwen.
The I'm A Celebrity hosts shared an update on social media on Sunday night joking: "We're celebrities... get us back in there!"
Donnelly added: "We're desperate to get back on the telly. The site was quite badly damaged during the storm and they are in there working round-the-clock to try and get us back up and running and back on air as quickly as humanly possible. But we don't know when that's going to be just yet.
McPartlin added "Fingers crossed."
A spokesperson for ITV said: "This is an on-going live situation and we're taking each day as it comes and working round the clock.
"Our priority is safely getting the whole site back up and running which means the show is back on air in the quickest time possible.
"We're currently not in a position to confirm when we'll be back on air but we'll absolutely keep you posted when we get more updates."
The contestants - including former Saturdays singer Frankie Bridge, Emmerdale star Danny Miller, Coronation Street star Simon Gregson, EastEnders actor Adam Woodyatt and retired footballer David Ginola - were removed from Gwrych Castle in north Wales, after the production base sustained significant damage during the stormy weather on Friday night.
Watch: I'm A Celebrity shows cancelled due to storm damage
The celebrities are required to quarantine individually while off site, in line with coronavirus restrictions and can return to the camp once the production has been safely restored.
Their removal from the site comes after TV presenter Richard Madeley was forced to quit the show after he fell ill last week.
The 65-year-old Good Morning Britain star was sent to hospital for a health, meaning he had broken the camp's COVID bubble and was not allowed back in.
The live shows on Saturday and Sunday night were replaced by a compilation show of highlights from previous years, hosted by Joel Dommett.
On Friday evening hosts Ant and Dec revealed that the show was unable to broadcast live due to the extreme weather conditions in north Wales, and joked about the unpopular highlights shows of previous years.
McPartlin said: "Because of Storm Arwen, for the first time ever we're not coming to you live."
Donnelly added: "This show was recorded earlier this evening because weather conditions are forecast to get worse.
"But don't worry, it's not like those hugely popular highlights shows we did on Saturdays last year, it's business as usual, this is the story of yesterday in the castle."
In 2020 - the series' first broadcast from north Wales due to coronavirus restrictions - the Saturday evening show was a compilation of highlights from throughout the week, which some viewers were disappointed by.
And Friday night's show saw 36-year-old musician Naughty Boy threaten to quit the show yet again, after facing another trial.
Watch: Who is Richard Madeley?