The duo will replace Kate Thornton and Zoe Tyler, who have apparently been axed as producers attempt to deal with a fall in ratings by revamping the programme, The Mirror reports.
Former Countdown star Vorderman is said to be taking over Thornton's role as co-anchor, while ex-Coronation Street actress Lindsay will fill Tyler's position as a panellist.
"Carol and Sally are a done deal," a source told the paper. "They were always popular choices, and bosses think they will be a perfect fit for the panel.
"They both bring a unique personality and sense of humour, which will hopefully sit well with the remaining regulars, but neither of them are afraid to speak their mind."
The insider added: "Loose Women has always been about lively debate, and these two are certainly not afraid of that."
Coleen Nolan will also exit the show at the end of the current series, while presenter Andrea McLean will return alongside panellists including Carol McGiffin, Denise Welch, Lisa Maxwell and Lynda Bellingham.
> Dawn French, Caroline Aherne for 'Loose Women'?