Nwaneri made Premier League history on Sunday when he became the youngest ever debutant in the competition's history.
Mikel Arteta brought him on for a brief cameo at the end of their 3-0 victory over Brentford, that sent them back to the top of the table.
The decision to hand Nwaneri his debut at such a young age has split opinion among talkSPORT pundits.
But Seaman believes Nwaneri has the ability and character to live up to his promise - so long as he is handled carefully like Ryan Giggs was at Manchester United.
The Arsenal legend is well aware of the teenager's talents too, having spent time observing him in training as an academy coach at the club.
"It's great for us to be making history, but you have to think of the long term," the legendary former goalkeeper said. "If you are good enough, you are old enough.
"He's got to be handled right off the pitch. He's a really good player, but you have to look after him.
"It all depends on how good you are and that's what determines whether you get a chance to play or not.
"I've seen this guy in training when I've been going in and coaching with the Under-23s and Under-18s. Honestly, you wouldn't believe his age."
When asked if he really one of the best he has seen, Seaman added: "He is at that age. He looks like he's a fully experienced pro. Then you find out how old he is… 15.
"He's that good, but still has to be handled right.
"Very similar to Ryan Giggs, he was handled perfectly by Fergie and look how good he turned out to be.
"It's about making sure he gets the right treatment off the field. He will certainly get it at the training ground and in games, he will be well looked after.
"He's that good that he can handle all that."
Arteta has not been afraid of playing the Arsenal youngsters, with the likes of Bukayo Saka and Emile Smith Rowe perfect examples for Nwaneri to follow.
Seaman added: "It will help him massively. We are now looking at them as experienced pros, they are still really young themselves.
"It's a great example for him to look at them two as an example and how they are treated, see what they are doing off the field.
"Agent-wise and all that sort of thing comes into it. Don't get away from what you do on the training ground and what you do in matches, that's most important of all."