Kris Engskov, the company's UK managing director, demanded urgent talks at Downing Street after Prime Minister David Cameron took a thinly veiled swipe at the coffee giant, the Sunday Telegraph said.
In a speech at the World Economic Forum in Davos promising to lead global action against tax avoidance, Cameron said it was time for businesses to "wake up and smell the coffee" about public anger.
Starbucks has been one of the highest profile targets of protests about "aggressive" tax avoidance after it emerged it paid no corporation tax in the last three years and only £8.6 million in 14 years of trading in Britain.
While the firm has since changed its tax arrangements so it will pay around £10 million in corporation tax this year, the revelations sparked a customer boycott and political accusations of immoral behaviour.
Cameron has faced a business backlash over his campaign, with Goldman Sachs chief executive Lloyd Blankfein saying the criticism risked "criminalising every right-thinking person who organises his or her affairs in a sensible way".
And Engskov was reported to have used the meeting to threaten to put on hold a planned £100 million investment in new UK branches of the coffee chain, which employs 9,000 staff in the UK.
A company source was quoted by the newspaper as saying Cameron was "singling the business out for cheap shots".
"A company that, it should not be forgotten, has pledged to pay tax now and into the future," they added.
Asked about the disagreement, Conservative Party chairman Grant Shapps told the Murnaghan programme on Sky News: "I don't think we would ever single out a single company but I do think companies in this country need to pay their way.
"I think they need to do what's right as far as that is concerned and I think most people watching this would agree, companies should pay their fair share of taxation.
"That applies to that company and anyone else you care to mention. It certainly applies to millions of smaller businesses in this country.
"People who work very hard, build up their companies from scratch..., are paying their fair share of taxes all the way through. The same rules have to apply to everyone."
A Starbucks spokesman said the meeting had been "long-scheduled" but declined to discuss details.
"Starbucks agrees with the Prime Minister that all businesses should pay their fair share.
"We employ 9,000 people, contribute £300 million worth of annual economic benefit and are forgoing tax deductions that will make the UK Exchequer at least £20 million better off."
Asked at the time whether the Davos remarks were aimed at Starbucks, the Prime Minister's official spokesman said the address "speaks for itself".