On the evidence provided in the first Test at Trent Bridge, where Anderson claimed five-wicket hauls in both innings in a man-of-the-match performance, it's impossible to argue with him.
Bowling well into the 140km/h range, swinging the ball both ways and showing commendable durability to deliver long spells, the only player on the planet who competes with Anderson for the title of "world's best" is South Africa's Dale Steyn.
But even accounting for England's love of South African imports, even if Steyn was on offer, it wouldn't matter because Cook wouldn't give Anderson up - for anyone.
"No not in any conditions now," Cook said after England's 14-run victory on Sunday. "That was very sub-continental conditions (at Trent Bridge) and he was outstanding.
"Swings it both ways on an immaculate length and makes it very hard to score."
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Anderson's love affair with Trent Bridge continued on the final day's play as he claimed all four Australian wickets to fall, finishing with a caught behind to remove the stoic Brad Haddin for 71 to seal the win.
The 30-year-old has 49 wickets at the Nottingham ground in just seven Tests at the enviable average of 17.
In this Test, he mixed the sublime, such as his gem of a delivery to remove Michael Clarke in the first innings, with the substantial - bowling a monster 13-over spell to start day five as his captain called on his frontline star again and again.
"When a bowler hits a rhythm, you just keep asking him if he's feeling alright," Cook said.
"That's why you do the training in the gym - that's the bottom line. When your captain needs you to do it, you are physically fit to do it.
"We know his skill but his heart to keep running in on a hot day on a flat wicket was outstanding."
Anderson's first-innings delivery to Clarke, in which he pitched a ball on middle but swung it away from the batsman and took the top of off stump, will be hard to beat for ball of the series - but even that achievement will be overshadowed by his lionhearted efforts on day five.
After his 13-over spell, Anderson needed to be treated for cramp during the lunch break, only to return to break Australian hearts.
"I knew It wasn't going to be a huge spell after lunch. They only needed 20 to win, so I think adrenaline plus that helped," Anderson said.