If he does, it will be a bitter-sweet moment for Cook who has been a protege and close friend of Gooch with both Essex and England.
"I wouldn't be here, or anywhere near, without his help," said Cook, 30, on Thursday.
"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 have.
"I wouldn't put myself anywhere near his class, but it would be a great moment. If I'm lucky enough to get that it will be a moment to remember.
"He's England's best ever and there'll only ever be one Graham Gooch."
Cook's comments on the eve of the second test came slightly more than a year after he had told Gooch that his services as batting coach were no longer needed.
"We both made a bit of a decision after we had worked together since I started on the Essex staff at 18 to look at different areas to work with different coaches.
"While it's really refreshing to work with different guys, it's also really important to have one guy to go back to, who knows your game inside out -- and knows you as a person.
"That's vitally important."
Cook has since repaired his relationship with Gooch and has consulted him regularly on his own batting.
"We always catch up about my batting," said Cook. "When you get scrutinised as much as you do and people are talking about your technique and game, it's very easy to get distracted and pulled in different directions.
"To have a guy who you trust, and have always worked with, I think is important for any batter."
Cook scored a meticulous 162, during nine hours of supreme concentration, in England's thrilling first test victory against New Zealand at Lord's.
It was his record 27th test century for England carrying his career aggregate to 8,869 test runs from 202 innings.
(Reporting by Steve Tongue; editing by Timothy Collings)
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