Cook, following his majestic 162 in England's 124-run win in the first Test against New Zealand at Lord's, now needs just 32 more runs in the second Test at Headingley, starting on Friday, to surpass Gooch's mark of 8,900 Test runs.
If he does it in this match, it will mean Cook have got there in 114 Tests compared to Gooch's 118, although Gooch arguably faced more genuinely all-time great bowlers throughout his career.
"However nice it would be if I do score 30, 31 32 or whatever it is to pass the great man that won't be enough for the game.
"If I'm lucky enough to get that it will be a moment I'll remember but if I am 30 not out it's important in a game situation I go on and get a big score," added the left-handed Cook, like the right-handed Gooch an Essex and England opening batsman.
More From This Section
"I wouldn't be here, or anywhere near here, without Goochie's help, so it will be slightly strange if I do go past his record because without his hard work and dedication to me and my game, I wouldn't have scored half the runs I would have done.
"It's a bit of a strange one. But there will only ever be one Graham Gooch. He's England greatest-ever batsman."
It fell to Cook to tell Gooch that he had been sacked as England batting coach in May last year.
"We worked together since I started on the Essex staff at 18 and then made that decision that I'll work on different areas and work with different coaches over a period," said the 30-year-old Cook, whose 27 Test hundreds are an England record.
"While it was really refreshing to work with different guys, I think its really important there's one guy you go back to because he knows your game inside out.