Rising party stars including Angela Rayner and Rebecca Long-Bailey were said to have been assessed for popularity as part of internal “succession planning”, according to The Sunday Times.
The paper also suggested leaked documents gave a scathing assessment of the embattled Labour leader, who was found to be “boring” and “fed up” by focus groups.
It also cited polling in the leaked document that rated veteran left-winger Mr Corbyn as the least popular of all current party leaders, including Ukip’s Paul Nuttall, who is standing in the upcoming Stoke-on-Trent central by-election.
Speaking on the BBC’s The Andrew Marr Show, Mr Watson said: “I only saw this story last night. People tell me that isn’t the case, it wasn’t road testing leadership candidates. There was a range of shadow cabinet members that were so-called road tested, this is what we do in our normal run of political consultations.
“I’m just slightly relieved they weren’t road testing me on the document that was leaked to the newspaper.”
When asked about a recent YouGov poll that suggested Mr Corbyn’s favourability ratings were plummeting, Mr Watson added: “This is not the time for a leadership election. He got a second mandate from our members last year, he is now the established leader of the Labour Party.
“It is his duty to lead the official Opposition through a period of unprecedented economic uncertainty and he will be tested.
“He has to explain those and he has to improve on them and he’s well aware of that.
“I do talk about the issues that I think Labour needs to address if we are going to narrow that poll gap.”
Labour earlier claimed the internal polling of voters in the North was intended as a routine measure to gauge the popularity of its politicians in the region and was not “succession planning”.
Mr Corbyn faces a further political headache from the claims, which follow a tranche of shadow cabinet resignations over the divisive Article 50 vote and reports of colleagues jostling for his position.
The leaked documents reportedly showed Ms Long-Bailey was said to be viewed as “passionate” and “very smart” by the public, while, shadow education secretary Ms Rayner reportedly received “overwhelmingly negative” feedback.
Mr Watson also questioned the timing of the resignation of Clive Lewis as not “particularly helpful” but welcomed the former shadow business secretary’s denial of rumours he was mounting a bid to topple Mr Corbyn.
Mr Lewis was the most high-profile rebel to resign from Mr Corbyn’s top team ahead of defying the leader on a three-line whip.
He voted against triggering Article 50 of the Lisbon Treaty, which formally starts the Brexit withdrawal process.
His actions provoked claims the Norwich MP was sounding out colleagues about a possible leadership run, but Mr Lewis rejected such talk.
“There has been speculation about that, and it is just that. You can quote me on this. It is total bollocks,” he told the Eastern Daily Press.
The Labour leader was forced to reshuffle his top team after a number of members quit ahead of voting against triggering Article 50.
However, 11 shadow ministers and three whips remained in their posts despite defying the leader’s command.
A large swathe of the parliamentary party ignored Mr Corbyn’s orders and tried to stop the Brexit Bill passing on Wednesday.
The 11 frontbenchers who voted against the Bill in its final Commons stage without quitting their jobs were Rosena Allin-Khan, Kevin Brennan, Lyn Brown, Ruth Cadbury, Rupa Huq, Chi Onwurah, Stephen Pound, Andy Slaughter, Catherine West, Alan Whitehead and Daniel Zeichner.
The whips were Thangam Debbonaire, Vicky Foxcroft and Jeff Smith.