Root is 2,457 behind Cook's mark of 12,472.

"He is a pleasure to watch, the most complete England batsman I have seen," Cook told BBC Sport.

"The person who could play the most incredible innings was Kevin Pietersen, but for the most complete batsmen in all three forms, it's Root. His consistency is incredible."

Cook was England captain when Root made his Test debut as a 21-year-old against India in 2012.

"He was a very good player of spin, as good as anyone," said Cook, who played 161 Tests for England. "That was obvious to see, even at that young age.

"He was ready to play international cricket. You knew he could handle the occasion."

Root's 115 not out against New Zealand at Lord's came in his 118th Test and made him the 14th player in the history of the game to achieve the 10,000 milestone.

At 31 years and 157 days, Root equalled Cook's record for the youngest player to reach the landmark, while he is the first to do so within 10 years of his debut.

"Barring injury, he'll go miles past my record," said Cook.

"He is so hard to tie down. I had to grind my way to 30, it always took me what felt like two hours. Because Joe has got so many low-risk scoring options, pretty much through 360 degrees, he will often get to 30 off 40 balls."

Left-hander Cook sits fifth on an all-time list topped by India legend Sachin Tendulkar, who made 15,921 runs in 200 Tests between 1989 and 2013.

If Root is to have a chance of breaking Tendulkar's record, he is likely to have to play at least 60 more Tests.

Given the greater amount of time given to white-ball cricket in the modern game, it might be that Root is the last player to have a realistic chance of overhauling Tendulkar.

Cook ended his international career at the age of 33 - just two years older than Root is now - but he believes their contrasting batting styles means Root will have a greater energy to play Test cricket at an older age.

"I would never have said I would finish at 33, but the time felt right for me," said Cook.

"The mental strain I felt to score runs took a toll on me. I'm not saying it's easy for him, but he doesn't seem to have that problem."