Citing unnamed "people briefed on the matter," the newspaper late Friday said Apple was considering investing into Twitter hundreds of millions of dollars, which could increase Twitter's valuation from $8.4 billion to more than $10 billion.
The contacts between the two companies' executives were not formal negotiations, and there were no assurances the two sides will come to an agreement, the report said.
Apple has already incorporated Twitter features into its software for phones, tablets and computers, The Times said.
Meanwhile, Twitter has assigned more resources into managing its relationship with Apple. the paper noted.
Apple's share of the US smartphone market was expected to inch up one percentage point to 31 percent this year, while the share for handsets powered by Google-backed Android software was expected to hit 41 percent, according to eMarketer.
On Tuesday, the company reported a rise in its quarterly profit to $8.8 billion on hot iPad sales but the results came up short of lofty Wall Street expectations, prompting its shares to dive.
The profit in the fiscal quarter to June was up 20.5 percent from a year earlier and amounted to $9.32 dollars a share, well below the consensus forecast of $10.36 dollars.
Revenues rose 22.5 percent to $35 billion, also below expectations of more than $37 billion.
Twitter, which allows its members to post brief comments, links or pictures, claims to have more than 140 million active users, with the largest number being in the United States.
A recent survey found one in seven Americans who go online use Twitter and eight percent do so every day.
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