It follows former newspaper editor turned Good Morning Britain presenter Piers saying he'd be up for the challenge - on one condition.
Piers said he'd take part so long as his early morning TV 'rival' Dan Walker did as well.
Dan currently fronts BBC's Breakfast show, airing at the same time as Piers on ITV.
Piers told the Daily Mirror newspaper: "I would seriously consider it if it meant giving Walker a lesson in how to dance in front of nine million people.”
Reacting to the news, another of Piers' rivals spoke up.
Lord Sugar tweeted "I would pay £25K to charity to see this plonker in tight pants dancing and another £25K if he makes it past the first 5 weeks.
"@piersmorgan he is as agile as a pregnant donkey," he added.
Piers quipped in response: "Not the first time you’ve paid to see a man in tight pants dance for you, is it, Shuggsy…"
Piers’ Good Morning Britain co-star Alex Beresford, who recently appeared on Dancing On Ice, also got involved.
He said: "With the greatest of respect he hasn’t got the balls @Lord_Sugar. Week 2 tops, and that’s only because you can’t get voted out week 1."
Lord Sugar added: "Yes Alex you are right. I hope the fellow at the BBC takes up the challenge then @piersmorgan is stuck for opening his big mouth.
"Force him to do it, embarrass him on @GMB @susannareid100 its up to £50K to charity."
It was previously claimed that Strictly bosses were interested in getting both Piers and Dan on the show: "Piers and Dan make Twitter digs at each other.
“It caught the attention of Strictly bosses, who want to tap into this rivalry. They think it’d be a ratings hit."
Neither would be the first breakfast TV presenters on the show: 2017 saw Piers' co-star Charlotte Hawkins take part while BBC's Naga Munchetty competed in 2016's series.
Strictly Come Dancing will begin on BBC One in the autumn.
The line up is typically confirmed around August/September.