While Anderson, England's highest Test wicket-taker, is full of respect for his team-mate Cook, he feels Hameed not only has a better technique but also the unflappable temperament that has played such a huge part in Cook's success.
"Is he as talented a player as I've seen come into the England side? I'd say so," Anderson said. "He's right up there.
"I know Cookie is the leading run scorer but I'd say he is a better more technically sound opening batsman that Cook.
"I played with him at Lancashire last year and you see teams throwing everything at him: short balls; around the wicket; everything. And he seemed to cope with everything that was thrown at him.
"From an opening bowler's point of view when you are sat in the dressing room and your opening batter has that calm way about him it just settles the whole dressing room.
"Bowling at him in the nets, he's so up to opening the batting, the way he plays it late, leaves the ball. I don't want to talk him up too much, but I think he's just a very exiting talent. And he has the temperament and concentration of Cook in bucket-loads. That mindset will stand him in good stead."
Such was the good impression Hameed made in India that it seems inevitable expectations on him will be increased markedly this season. But while some players might buckle under the pressure, Anderson expects Hameed to flourish this summer and in Australia at the end of the year.
"I'm sure Australia will throw everything they've got at him," Anderson said. "Pace, short balls, aggression, verbals. I'm sure they'll go at him. They usually pick on the young guys. But with his calm nature I think he'll be able to handle it.
"He's such a calm, level-headed lad I don't think he'll need much help. He's very switched on for his age. He's got a good solid family behind him that help him a lot. He's got all the attributes to be able to cope with anything that's thrown at him. His ability and his talent is frightening for such a young lad, so I think he'll cope with anything."
Anderson was looking forward to bowling at Cook before a hip injury ruled out the former England captain from the opening round of County Championship matches. It would have been the fifth time the pair have come against one another in the Championship and Anderson has had much the better of their encounters. On the most recent occasion, in 2015, he trapped Cook leg before for 1 in the third over of the match, while in the previous game, in 2010, it took him until the fifth over of the match to dismiss him for 3. And while Cook made a second-innings half-century, it could not prevent Lancashire winning by eight wickets and Anderson finishing with nine in the match.
Cook's injury removes the potential for some lively scenes in the middle with Anderson, a bowler who likes to share a few words, admitting he would have found it hard to keep quiet.
"I've bowled at him for well over 10 years and I just feel like I'm going to get him out," Anderson said. "I know his game so well. I find it hard going back into county cricket and playing against people you've never seen before. So when you come up against someone like that who you've known for so long, I find it fun.
"I've played against him three times, I think, and got him out each game. But in one game he got runs before I fluked a wicket and got him caught on the hook.
"I think a few of the lads gave him a send-off. It must have been just after he got a double-hundred for Essex against Australia in 2005 so we thought he was an arrogant little so-and-so so we told him. It turns out he's not."
Meanwhile Anderson revealed he had "made peace" with the fact that his international limited-overs career is over. But he does expect to be in white-ball action for Lancashire in the coming weeks in a bid to ensure he is fully fit by the time the Test season begins in July. And he hopes there could still be a white-ball recall for Stuart Broad.
"I'm going to play 50-over cricket for Lancashire in May," he says. "The way the season is mapped out, to have the month of May off completely would be foolish. It wouldn't help me at all. So I'm playing two out of the first three Championship games and then I'll reassess.
"I've kind of made peace with the fact that I probably won't play again. In my head I'd still like to because I think - although I've had injury problems over the last twelve months - I could still get to that World Cup in 2019.
"But the way the team has moved on in the last 18-months, it would probably not be the way they're looking at the team for me to come back in. Stuart Broad coming back in would make sense, because it looks like the bowling attack needs that senior figure. He's only 30 and he could make it to the World Cup quite comfortably."
While Anderson accepts "I can't bowl 90mph any more like I used to" he still hopes to play a role in the Ashes at the end of the year. He has been impressed by Australia's development, though, and has particular respect for their captain, Steven Smith.
"Australia look like a really promising team," he said. "They're obviously building something at the minute. They look pretty strong, especially in the batting.
"Smith is really tricky to bowl to, because he's so unorthodox. You think you've got a chance with him all the time, but he's a really talented batsman. He's turned himself into a brilliant batsman and he's a key player for them, being captain as well. When he scores runs, they generally get big scores.
"You think you can get him out all sorts of ways. You think you can york him leg-stump, because he walks that far across. But he manages to get bat on it.
"It is going to be difficult for us, and I think now we've seen how he bats, over the next few months we can come up with some plans for him."
Jimmy Anderson was speaking on behalf of BRUT Sport Style, the new fragrance from men's grooming brand BRUT