The former pacer lauded the new Indian left-arm quick after a promising debut in Canberra.
Ghavri, himself a practitioner of the left-arm angle and someone who would know of fast bowling better than most, thinks Natarajan can serve Virat Kohli's team for a long time.
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"Natarajan is looking like a bright prospect for the Indian team," Ghavri told Times of India. "He is very talented. If he keeps on bowling well and keeps up his fitness levels, he can serve Indian cricket for a long time. He is a bright prospect for the Indian team."
"He has the ability to generate a good amount of pace. He has got some variations. The best part is that he has the ability to bowl yorkers, especially in the death overs. He has all the qualities a left-arm pacer needs."
"I know he (Natarajan) gave away a lot of runs but he has taken wickets too. He bowled yorkers in the death. That controlled the flow of runs. He looked good to me in his debut match. I am sure he will go a long way," he added.
Natarajan made his international debut at the age of 29 with the third and final ODI against Australia on Wednesday (December 2). He delivered a promising spell of 2/70 in India's consolation 13-run victory in Canberra.
Originally picked only as a net bowler for the tour, Natarajan found himself included in the T20I squad when finger-spinner Varun Chakravarthy had to be left out due to injury and later also the ODI touring contingent when pacer Navdeep Saini complained of back spasms.
Like Chakravarthy, the right-arm quick impressed many with his defensive bowling skills during the IPL 2020 in UAE. Natarajan emerged as one of the better Indian pacers with his death-overs exploits, especially the ability to consistently nail the yorker.
"The way Zaheer did under Ganguly's captaincy, Natarajan can do well under Kohli's captaincy," said Ghavri in a huge vote of confidence. "Kohli is a good leader and I am sure he will motivate this guy (Natarajan) and make him learn."
"As he progresses in his career and if plays with consistent performance, he is going to serve the Indian team for a long time. He is a sparkling prospect for India."
At his age, Natarajan hasn't had the body of work you would expect a bowler to have at the first-class level. But for Ghavri, as long as the pacer maintains his fitness, he'll be fine at the international stage.
"Age hasn't got anything to do with cricket as long as somebody is really fit enough to deliver the goods," Ghavri said. "Even though he is 29, (if) he goes on to play for India for another 6 or 7 years, that means he is doing a good job. He should be fit and perform for the team, that's all."
"I will just advise him to keep his fitness level high. If he manages to do so, he can serve the Indian team for long. He can fill the left-arm pacer void in the Indian team".
"Khali gym jaake body banana jaruri nahi hai (Going to the gym and working out isn't enough). Cricket related exercise is very important. If he is a fast bowler, he should be bowling at the nets for at least an hour and a half. The more he will bowl at the nets, the more he will improve."
"He should bowl at least 15 to 20 overs in a day. That's how you prepare yourself. You are playing for your country, not domestic cricket," he signed off.