Desmond, who also owns the Daily Express and OK! magazine, has been discounting the tabloid to 20p in certain parts of the country since November 2008.
Now he is to put further pressure on tabloid rivals, by cutting the cover price to just 10p from 1 July.
The Daily Mirror sells at 45p a copy and Trinity Mirror chief executive Sly Bailey has long railed against competitors that have slashed their cover price to lure readers.
The Sun is price-discounting to 20p from 30p in certain parts of the UK, including London, Birmingham and Oxford.
The Daily Star's price-cutting has benefited its circulation and the title has been – in terms of circulation – one of the few success stories in the newspaper industry.
According to the latest audited figures, circulation of the Daily Star rose on the year by 0.87% to 827,005 in March. The Sun sells around three million copies a day, while the Daily Mirror sells about 1.25 million.
Desmond believes he can overtake the Daily Mirror's circulation by price discounting.
Desmond, who has set aside £5m to cover the cost of cutting the Star's cover price, will be sacrificing hundreds of thousands of pounds in revenue.
In an interview in The Sunday Times, he said: "I want to really go for it now. We are a private company and we have loads of dough."
In the interview, he also commented on his reported interest in making a bid for ITV, saying: "I am not gong to get involved in something where I can't turn it around quickly."
When asked who he is supporting in the General Election, Desmond said he and the Express are backing the Conservatives. He said: "If they don't get in, we are fucked, fucked, fucked."