LONDON — The cloud businesses of Amazon and Microsoft could face stricter scrutiny from European Union regulators, who are looking into whether they should fall under the bloc’s dragnet on Big Tech companies.

The bloc’s executive Commission said Tuesday that it’s assessing whether Amazon Web Services and Microsoft Azure should be classified as “gatekeepers” under the EU’s Digital Markets Act.

The sweeping rule book is designed to rein in the market power of tech companies with a list of do’s and don’ts, under threat of hefty penalties.

Gatekeepers face extra obligations under the DMA and regulators have already given the label to other parts of the two companies, such as Amazon Marketplace and Microsoft’s LinkedIn. The designation is based partly on user numbers, which makes it harder t

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