Cook has followed in Gooch's footsteps, and benefited from his long-term guidance, first at Essex and then as a record runscorer and leader for his country.
On the day England also announced the first squad of Peter Moores' second tenure as head coach - to face Scotland in a one-day international in Aberdeen on May 9 - the captain found himself reliving last weekend's conversation with Gooch.
Cook admits it was a daunting prospect to inform the man he has looked up to for so long of his and Moores' decision to call time on him as batting coach.
"Everyone knows how close we are - and we've been through quite a lot together," Cook said. "To make a decision on a guy I've had so much respect for was tough. I was telling a man, who I used to go and queue up to get his autograph and hope he'd score runs, that it's time to move on. I'll remember that for a long time."
The likelihood is Gooch will be replaced shortly. But Cook still expects he and some of his team-mates will retain their association with the 60-year-old, the latest key figure to depart the scene following last winter's Ashes whitewash.
"I hope that relationship will continue - not just with me," Cook said. I know Belly [Ian Bell] has used him a hell of a lot, and has had great rewards, and we hope we can continue doing that on a one-to-one basis."
Since the end of the Ashes, England are also minus Andy Flower as team director and, of course, their other record runscorer Kevin Pietersen. Limited-overs coach Ashley Giles is gone too, having lost out to Moores to effectively replace Flower.
The first squad, 13 strong, in Moores' new era is notable for the inclusion of just one uncapped player, Nottinghamshire seamer Harry Gurney, and returns for Gary Ballance, his fit-again fellow Yorkshire batsman Joe Root and Test linchpin seamer James Anderson.
England ODI squad (v Scotland, Mannofield, Aberdeen, May 9) A Cook (capt), M Ali, J Anderson, G Ballance, I Bell, R Bopara, J Buttler. H Gurney, C Jordan, E Morgan, J Root, J Tredwell, C Woakes