A No 10 spokeswoman said the current regime is "unclear" and does not give the government enough options to "get the best deal for the UK" from foreign investors.
During her campaign for the Tory leadership, Mrs May singled out US pharmaceuticals giant Pfizer's abandoned £69 billion takeover bid for Anglo-Swiss drugs giant AstraZeneca in 2014.
The PM said on 11 July that the government had "almost allowed" AstraZeneca to be sold to Pfizer, which had a track record of asset-stripping.
She said reforms were needed that allow the government to "defend" a sector that is facing threat in a speech in which she also mentioned Kraft's takeover of Cadbury.
Following reports that the regime governing foreign investment would be tightened up, a No 10 spokeswoman said: "The PM has been clear that the vote to leave the European Union was not a vote to turn inwards, and in fact we have the opportunity to forge a new global role for the UK.
"Our industrial strategy will enable the UK to be a great place in which to invest and do business, and we are keen to work with businesses on improvements.
"We want foreign direct investment to boost UK jobs and support businesses here to grow on the world stage.
"But at the moment our regime is sometimes unclear, leaving investors without certainty and the government with few options to scrutinise in order to get the best deal for the UK.
"Improving the regime would be good for business as well as being good governance."
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