Cook became the 12th player in history to score 10,000 Test runs during England's nine-wicket win against Sri Lanka at Durham last month but he is nearly 6,000 runs short of Tendulkar's record aggregate of 15,921 runs from 200 matches.
The left-handed opener, 31, broke Tendulkar's earlier record of being the youngest to score 10,000 Test runs by more than five months.
"Six thousand runs is a long way away. It was set by an incredibly talented genius. I'm no genius and Tendulkar is, so that is a long way ahead," Cook said at the Lord's ahead of the third Test against Sri Lanka.
"I want to play for England for as long as I can and at the moment I'm really enjoying it. I am really motivated and hungry and where that takes me who knows."
The England skipper has 28 Test hundreds to his name at an average of 47, whereas Tendulkar bowed out of Test cricket with a record 51 centuries at an average of nearly 54.
Former India captain Sunil Gavaskar, the first man to score 10,000 Test runs, said last week that Cook had it in him to set a new aggregate record for most Test runs because of his age and the fact that England play more games over the long format than many other nations.
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