Twitter was valued at $8.4 billion last year, but it Apple were to invest it could elevate its value to $10 billion, unnamed sources told The New York Times.
Although Twitter bosses are said to be open to the discussions, the company does not need the cash. With more than 140 million active users every month, advertising revenue is said to be at an all-time high.
Dick Costolo, Twitter’s chief executive, recently said the American company had “truckloads of money in the bank”, with reports suggesting more than $600 million was stashed.
In another interview he conceded that despite their healthy finances Apple would be "a great partner". "We think of them as a company that our company looks up to,” Mr Costolo said.
Speculation about a partnership comes amid growing competitive threats from Facebook – which is aligned with Microsoft – and Google.
Apple buying a stake in the social-networking site could still be a long way off, however, the discussions are said to be only in their early stages and a long way off making any negotiations.