The Labour leader visited the Whitaker museum in Rossendale as part of his tour of Tory marginal seats.
He visited a children's art workshop at the museum, where Isla McChesney, 7, asked him: "Excuse me, when are you going to be Prime Minister?"
Mr Corbyn replied: "Well, that depends on when we have an election. It's a good question."
He was also given a tour of the museum by managing director Carl Bell and was shown work by contemporary artist Gordon Cheung.
Mr Corbyn is visiting around 40 seats over a summer campaign during the parliamentary recess as he seeks to build on Labour's momentum from June's general election and keep up the pressure on Theresa May.
Mr Corbyn visited the museum, in the constituency of Rossendale and Darwen, after stopping at a foodbank in Bolton on Thursday morning.
He visited The Hope Centre, part of St Andrew's Church in Bolton, which provides kids' clubs, a foodbank and community support.
Mr Corbyn chatted to residents and a women's group inside the centre about Labour's policies and their concerns over local bus routes being cut, the bedroom tax and the need for more social housing.
He told them: "It's a way of looking where policies are going wrong but also a way of looking at how we will develop our much more detailed policies... our manifesto was put together in very short time, it had to be, it set out a bold, general picture.
"I then want to put the detail together on housing, on benefits, on community improvements and transport.
"I promised I would take the message out to the country because this Government only has a very small majority courtesy of the DUP; we don't think it can survive forever.
"I think it's important to get the Labour message out across the whole country so I'm travelling all around.
"I was in (the) South West last week, I'm in (the) North West this week, in Scotland next week."
He is due to appear at an open-air rally in Nelson, Lancashire, on Thursday evening.
On Friday he will visit Blackpool and Morecambe before holding a rally on the beach at Southport.