The 31-year-old left-handed opener needs just 36 more runs to become the first Englishman -- and only 12th player overall -- to score 10,000 runs in Tests and he will hope to get there during this week's first Test against Sri Lanka at Headingley, which starts on Thursday.
"It would mean a lot and hopefully I can get there sooner rather than later so we can talk about something else," said Cook, speaking at Headingley, Yorkshire's headquarters in Leeds, northern England, on Wednesday.
The last time England played Sri Lanka in a Test at Headingley, two years ago, was one of the low points of Cook's career.
Sri Lanka, inspired by a brilliant hundred from captain Angelo Mathews -- still their skipper -- won a thrilling match by 100 runs off the penultimate ball of the game to secure their first Test series win in England.
- Tough moment -
================
But the Essex batsman decided to carry on and has since been rewarded with last year's Ashes success and a series win in South Africa during England's most recent Test series.
"It was a game of fine margins and Sri Lanka came out on top and thoroughly deserved it," he said as he recalled the 2014 Test at Headingley.
"It was a real tough moment for me as a captain, there's no doubt about that, but I'm glad I hung in there for what's happened since.
Sri Lanka are still getting used to life withour star batsmen Kumar Sangakkara and Mahela Jayawardene, who between them amassed more than 24,000 runs in Test cricket before they both retired from international duty last year.
"They're irreplaceable but sides move on and evolve," said Cook.
"Sri Lanka have got a history of punching above their weight and are really, really competitive, no matter what's gone before.
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