Cook became the 12th player in history to score 10,000 Test runs during England's nine-wicket win against Sri Lanka at Durham on Monday to take an unassailable 2-0 lead in the three-match series.
The opener was also the first Englishman to achieve the feat and, at 31 years and 157 days, the youngest to get to the landmark, breaking Tendulkar's record by more than five months.
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Currently Cook (10,042 runs in 128 Tests) is 5,879 runs away from Tendulkar's record and Gavaskar, who was the first to register 10,000 runs in Test cricket, believes the Englishman can chase down the target.
"Cook can break Tendulkar's record of Test runs. He has age on his side and England play more Tests," Gavaskar told NDTV.
"Given the number of Tests England play every year and if Cook can hold on to his form in the next seven years, he can surpass Tendulkar," he added.
England are one of the busiest of the Test-playing sides and Cook will have ample opportunity to add to his tally in the coming months.
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England play one more Test against Sri Lanka at Lord's next week before then taking on Pakistan in a four-match series.
Cook's team then embarks on tours to Bangladesh and India, where they will play a total of seven Tests.
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