One source said Drahi had said he also saw the UK as ripe for investment because its fibre broadband rollout is behind that of other major countries like France.
He bought his stake just weeks after BT struck a deal with UK regulators on the prices it was allowed to charge for access to its new fibre network.
That meant BT chief executive Philip Jansen could pledge to spend £15 billion to cover 25 million premises by December 2026.
One source said the reason for the meetings was to explain his background as having installed fibre to millions of households and businesses in Europe, the US and elsewhere.
He has told ministers he feels he and his company Altice can “help BT move faster” in its rollout.
Some in BT believe his overtures to the government could indicate that he is not interested in just being a “sleeping shareholder” but is planning something more dramatic such as a takeover of BT.
He has told the Takeover Panel he does not intend to buy the company, a notification that lasts six months.
Drahi has a reputation for having done multi-billion dollar deals largely funded by debt.
He is known to have strong connections with US financiers and some have speculated that he could easily raise the funds to buy BT, which is valued at nearly £19 billion.
Ministerial sources said a deal for BT would definitely come under government scrutiny as the nation’s telecoms infrastructure is a vital national security asset.
Another source said while Drahi was practiced in doing large, debt fuelled takeovers, he was also cautious in his business practices.
However, they added: “He’s also not just going to sit there with a 12% stake, saying: ‘Jolly good, you just carry on as you were.”