He said the "golden circle of the media establishment" was "obsessed" with leadership questions, whereas voters were more concerned with inequality.
Pollsters have suggested Labour could lose about 150 seats.
Mr Corbyn also said an anti-Semitism row in Labour was being "dealt with".
He pointed to an inquiry led by Shami Chakrabarti, former head of campaign group Liberty, and said "only a very small number" of cases of anti-Semitism had been identified to date.
On Thursday, Labour will be defending the large council gains it made in 2012, the last time the seats were contested.
"We are not going to lose seats," Mr Corbyn said as he launched his party's election poster.
"We are looking to gain seats where we can, but these elections are being fought on the issues of every different community across the country."
Mr Corbyn overwhelmingly won last year's Labour leadership vote despite lacking the support of most of the party's MPs.
On Sunday, Mr Corbyn's ally Len McCluskey said the anti-Semitism row was being used by opponents of Mr Corbyn within Labour to undermine his leadership.
Asked about reports of a possible leadership challenge, Mr Corbyn said: "I'm here. I'm going on," replying "of course" when asked if he would stand in a leadership contest if there was another one.
People in the media were "obsessed" with the leadership question, he said, advising people to focus instead on the "grotesque level of inequality".
He added: "It's time that many in the golden circle of the media establishment actually got out a bit and listened to what people are saying."
Jeremy Corbyn has predicted Labour will not lose any seats in Thursday's English council elections and dismissed reports of a possible challenge to his leadership if results go against him.