The Labour leader made the extraordinary claim as he was forced to defend his support of the hardleft firebrand.
He was challenged for his repeated support of his predecessor and for claiming he would have made a "great Prime Minister" during last night's BBC Question Time Leaders' Special.
"It wasn't a question that really arose because I didn't think we were going to win the election," Sir Keir said on the programme.
But when host Fiona Bruce asked for a yes or no answer as to whether he meant it, the audience laughed when he didn't give one - and instead said Mr Corbyn would be a better PM than Boris Johnson.
Under intense grilling, a squirming Sir Keir also refused to reveal a number target by which Labour would reduce net migration.
Problem
"We want to get it down significantly. It needs to be balanced immigration so it works for our economy and works for our country," he said.
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