Peter Kyle dined with Sam Altman in March and April of this year, according to transparency data released by the government.
In a recent podcast interview with former Downing Street adviser Jimmy McLoughlin, Kyle said he has to deal with "global companies which are innovating on a scale the British state cannot match".
The deal comes as the UK government looks for ways to improve the UK's stagnant economy, which is forecast to have grown at 0.1% to 0.2% for the April to June period.
In January, Prime Minister Keir Starmer announced an "AI Opportunities Action Plan" designed to boost growth, which was backed by many leading tech companies.
At the time, Tim Flagg, chief operating officer of UKAI - a trade body representing British AI businesses - said the proposals took a "narrow view" of the sector's contributors and focus too much on big tech.
The UK government has made clear it is open to US AI investment, having struck similar deals with OpenAI's rivals Google and Anthropic earlier this year.
It said its OpenAI deal "could mean that world-changing AI tech is developed in the UK, driving discoveries that will deliver growth".
It already uses OpenAI models in a set of AI-powered tools designed to increase productivity in the civil service, dubbed "Humphrey".
The Labour government's eager adoption of AI has previously been criticised by campaigners, such as musicians who oppose its unlicensed use of their music.
Generative AI software like OpenAI's ChatGPT can produce text, images, videos, and music from prompts by users.
The technology does this based on data from books, photos, film footage, and songs, raising questions about potential copyright infringement or whether data has been used with permission.
The technology has also come under fire for giving false information or bad advice based on prompts.