Gasparino claimed the board is "concerned" the speed of innovation seen during the second Steve Jobs era, which resulted in the iPod, iPhone and iPad change the tech world, has not continued under Cook.
He said: "What have they had lately? They have had the iPad, they've had a few other things, but they don't have anything innovating from what came from Steve Jobs.
"And that concern is basically manifesting into pressure on Tim Cook to innovate — do something fast," added Gasparino who said the concern hasn't reached the point that Cook's job is under threat.
Cook on the clock?
Cook himself has claimed new products are coming later this year, most likely at an iPhone launch event on September 10, although those launches are likely to be tweaked versions of existing products.
There is a genuine feeling that Apple's long-standing lead in innovation has been eroded since the late Steve Jobs was forced to relinquish the top job due to ailing health.
Apple itself is conscious of the mutterings. During the launch of the new cylindric Mac Pro at WWDC this year, the company's bombastic marketing chief Phil Schiller blasted: "Can't innovate anymore, my ass!"
Does Apple still have the ability to wow us with yet another epochal product launch any time soon or is the rumoured pressure on Tim Cook to be more like Steve only going to grow?
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A technology journalist, writer and videographer of many magazines and websites including T3, Gadget Magazine and TechRadar.com. He specializes in applications for smartphones, tablets and handheld devices, with bylines also at The Guardian, WIRED, Trusted Reviews and Wareable. Chris is also the podcast host for The Liverpool Way. As well as tech and football, Chris is a pop-punk fan and enjoys the art of wrasslin'.