Cook fell for 17 in England's disappointing first innings at the Ageas Bowl to continue a lean summer where he has only passed fifty once. It is part of a longer theme in Cook's recent career where the occasional peak - double centuries against West Indies and Australia - have come amid extended runs of low scores.
"My concern would be watching him that I don't see any improvements in his game," Gooch told the Today show on BBC Radio 4. "I think he's flat-lining a little bit. When you're a batsman, you need to improve yourself, you need to look for new things to do to drive you forward."
In the last five years of his Test career, Gooch averaged 51.55 compared to his overall figure of 42.58 making 12 of his 20 hundreds in that period including the career-best 333 against India at Lord's.
Such has been the longevity of Cook's career, which has included multiple occasions where he has hauled himself out of lean runs, it has often been suggested that he could emulate the Gooch's late-career surge. He overtook Gooch as England's leading Test run-scorer in 2015.
"I don't know how he's practicing and I don't know what he's doing away from the game, but I am concerned when I see him play," Gooch said. "I think he makes similar mistakes but even at 33 or 34, you can improve yourself."
Cook is currently averaging 19.06 in 2018 having had a poor series in New Zealand and then finding problems against India's impressive attack. His lean form has compounded England's opening problems which, since Andrew Strauss' retirement in 2012, have focused on trying to find a reliable partner for Cook without success, a cycle which looks set to continue unless Keaton Jennings hauls himself out of his current struggles.
Before the fourth Test against India, Cook received fulsome support from the current captain Joe Root when it came to the remainder of this season. England's overseas assignments in 2018-19 include Test series against Sri Lanka and West Indies