In an interview to The Telegraph, Arthur revealed he loves watching Kohli whenever he comes out to bat and even termed the 27-year-old as an interesting captain.
"I love watching Virat (Kohli)... He's phenomenal and is one batsman I sit down and watch whenever he comes to the crease. He's right up there with the best I've seen... I still recall his 141 in the second innings of the Adelaide Test almost two years ago. He'd got a hundred (115) in the first innings as well," he said.
Kohli became the first Indian Test captain to slam two double hundreds after hitting 211 against New Zealand at Indore.
Praising the aggressive Indian skipper's captaincy Arthur said, "Virat's an interesting captain... He's exuberant and very passionate about what he does. His passion for the top job comes through in abundance."
When asked about his views on India taking over the No. 1 spot from Pakistan in Test rankings, Arthur was quoted as saying, "Rankings don't reveal everything, but are an indication of the success you taste as a team... Other things too have to be taken into account... As coach, I want every player to get better and better. I get the maximum satisfaction when I work with a young player and he responds with performances. More than the rankings, it's about competing at a certain level and attaining success. I can cite the example of Younis."
India recently dethroned Pakistan to become No. 1 Test side after beating New Zealand in the three-match series.
Misbah-ul-Haq-led Pakistan are playing their first ever day and night Test against West Indies at Dubai.