The pro-EU peer and journalist branded the backbencher an “absolute throwback” and claimed his appointment would spell “the end” for the Conservative party.
The politician spoke to LBC’s Andrew Pierce after the Brexiteer reportedly told a friend he wanted to become the Tory leader.
Donald Trump ally and academic Ted Malloch told the Mail on Sunday he went for a private lunch with Mr Rees-Mogg, who reportedly expressed interest in the role.
He added: “He did not mean now but at some point in the future.”
Responding to the prospect the Eurosceptic MP taking the reins, Baroness Wheatcroft said Mr Rees-Mogg did not have what it took to attract younger voters.
She said: “Jacob’s immensely entertaining, incredibly polite, as you say, he’s very good company but he certainly hasn’t got what it takes to attract the votes of my children because he is absolutely a throwback.
“Not just in his manners but in his attitude.”
She branded the politician “divisive” before saying she could not imagine him becoming party leader.
Baroness Wheatcroft said: “If Jacob Rees-Mogg became party leader, the Tory party would be absolutely killed, it would be the end because he would be such a divisive figure – I really can’t imagine that happening.
“I think he’s very serious, I think he’s an ambitious young man… he’s very clever as I say, he’s plotted his route just as carefully as Boris Johnson did – he could come off the rails just as Boris did.”
However, despite the speculation, Mr Rees-Mogg has continually played down the idea and previously told the radio station he had already achieved his “life’s ambition” of becoming the MP for North East Somerset.
He added: “I’m a huge admirer of the Prime Minister – I want her to stay in office.
“I back her very strongly, we need stability, we need a period of calm – we’ve had some very exciting summers over the last few years and I think we need a calmer, cooler summer regardless of the temperature outside.”