It is reported to own a 49% stake in the company, which is at the forefront of artificial intelligence development.
The Competition and Markets Authority (CMA) wants to review whether the partnership has led to an acquisition of control, if a de facto merger has taken place, and if this could impact competition.
It has asked interested parties – which could include rivals like Google – to comment on the arrangement with a view to potentially launching an investigation.
Mr Altman briefly joined Microsoft during his five-day exile from the company he co-founded in 2015, and the CMA said the saga had partly influenced its decision.
Upon his return, it was announced the Windows maker would take a non-voting position on OpenAI’s board.
Microsoft president and vice chair Brad Smith downplayed the arrangement, saying it was “very different from an acquisition such as Google’s purchase of DeepMind in the UK”.
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Google bought that company in 2014, when there was far less mainstream scrutiny of the AI industry.