He added: “As a Tory member, I would like to extend a welcome to the Leader of the Opposition with open arms.”
The Tory former minister was commenting after Rishi Sunak suggested Nigel Farage would be welcome to join the Conservatives – insisting his party was a “broad church”.
“The more pressing question is not whether Nigel Farage will join the Tory Party, but whether Keir Starmer is planning to defect and launch a Tory leadership bid,” he told GB News.
A Labour spokesman said: “What Jacob Rees-Mogg knows is that the travel is all in the opposite direction with former Tory voters backing Keir Starmer’s changed Labour Party to end thirteen years of Tory decline and give Britain its future back.”
The Labour leader sparked a backlash with his article, in which he said Mrs Thatcher had effected “meaningful change” and “set loose Britain’s natural entrepreneurialism”.
He also sought to outflank Mr Sunak by appealing to Tory voters on Brexit and migration.
In a shift from his staunch opposition to Britain leaving the EU, Sir Keir said the Tories have “failed to realise the possibilities of Brexit”.
He said he “profoundly disagrees” with the idea Labour should duck topics such as small boat crossings and immigration.
And he added: “This is a government that was elected on a promise that immigration would ‘come down’ and the British people would ‘always [be] in control’. For immigration to then triple is more than just yet another failure – it is a betrayal of their promises.”
Sir Jacob, who served as business secretary under Lizz Truss, said: “A man wrote an article for The Telegraph last week entitled ‘Voters have been betrayed on Brexit and Immigration.’
“This reads as if it were vintage Farage. The man in question went on to hail Margaret Thatcher, as the leader who dragged Britain out of its stupor by setting loose our natural entrepreneurialism.
“He then went on to criticise the wasted money, the high debt and the record-high tax burden. He sounds as if he could be a member of the ERG!”
Sir Jacob added: ““So, who is this man? This great Conservative-sounding figure? Is he a cabinet minister waiting in the wings for a Tory Party leadership bid? One setting out his stall – along with a number of other ministers who seem to be circling.
“He must be among the most ardent of Eurosceptics, a member of the ‘Go for Growth’ movement, a Thatcherite – a Trussite even – a capitalist, a sensible, free market Conservative.
“But – the man I’m referring to is not Nigel Farage, Boris Johnson, Liz Truss or even me, for that matter.
“I’m of course talking about the leader of the Labour party – the socialist party – Sir Keir Starmer.”