Tory policy currently rules out increases in income tax, national insurance contributions and value-added tax (VAT), but May refused to say the pledge will be included in the party's manifesto for the General Election in an interview with the BBC.
She said: "I don't want to make specific proposals on taxes unless I'm absolutely sure I can deliver on those."
However, May said her party will commit to not raising VAT in an interview with ITV.
The tax lock promise has been widely criticised by economists as an unnecessary restriction on a chancellor which does not allow governments to easily raise revenues if circumstances change.
If the promise is not included in the manifesto it would pave the way for tax increases in the event of a Conservative majority.
However, May said she has "absolutely no plans to increase the level of tax" and that it was her "intention to reduce the tax burden on working families".
The pledge was introduced by former Prime Minister David Cameron in 2015 as he looked to fend off the challenge of the Labour party under Ed Miliband at the last General Election. However, reports have emerged the chancellor Philip Hammond is keen to remove the restriction as he aims to balance the books.
While the government's deficit fell to its lowest point since the global financial crisis in the 2016/2017 tax year, borrowing has remained higher than the party had promised. The chancellor was on course to miss his target of balancing the books during the next Parliament (before an election in 2025) before the snap election was announced.
May also said the state pension will go up "every year", although said she would not reveal how much it would increase by until the Conservative party manifesto is launched.