Root, 33, overtook Cook's record England tally of 12,472 runs in the first Test of the ongoing series in Pakistan, in which the Yorkshireman scored a mammoth 262.
He is now fifth on the all-time list of runscorers behind Sachin Tendulkar, who leads the way with 15,921, Ricky Ponting, Jacques Kallis and Rahul Dravid, all of whom have retired.
"I think Joe Root could set a mark, certainly on the English side, which will be very hard to beat," said Cook, who retired from Test cricket in 2018 with a century in his final innings.
"But you just never know. I hope he can get very close, if not be the first person to score 16,000 Test runs. It would be a great achievement but it's a fair way off yet."
Cook, 39, said even in a fast-changing landscape, with Test cricket competing for calendar space alongside the white-ball game, it was difficult to say records would stand forever.
"Everyone looked to that Tendulkar record of 200 Test matches and I think quite a few people said, 'Well, that's never going to be done'.
"And you've got a fast bowler who has played 188 Test matches and taken more than 700 wickets (retired England quick James Anderson).
"So I know the game is changing, the landscape is changing. But something always crops up, someone always does."
'Big Four'
Cook said it was difficult to separate the so-called "Big Four" of Root, India's Virat Kohli, Steve Smith of Australia and New Zealand's Kane Williamson.
"They're all wonderful, wonderful players, all very different actually in terms of their methods and ways of playing," he said.
"But one thing which kind of unites them is that hunger and desire to keep improving and keep churning out the runs.
"They are generational players who will always be spoken about, and the fact that you can add Joe Root, whether you put him first, second, third, fourth, all personal opinion, it doesn't really matter.
"But they are great, great players and make the game, the kind of one which we all started playing, look a lot easier than it is."
Cook on Wednesday became the 113th payer to be inducted into the International Cricket Council's Hall of Fame, joining alongside retired India spinner Neetu David, a star of the women's game, and South African multi-format great AB de Villiers.
"It was a surprise," said the former England skipper. "When you read the list of people that you're joining, it's a great list to have joined. So I feel very privileged."
Cook paid a warm tribute to former England captain Graham Gooch, a predecessor at his county side, Essex.
"A lot of people know about my relationship with Graham Gooch, Essex and England opener and kind of mentor, friend, coach, you name it," he said.
"He's kind of done everything for me. So it's just we never played on the same team. I thank God, probably. Thank goodness, because he was obviously a far better player than me."
