While Faletau is yet to win his first cap, Brew made his last appearance during Wales' autumn draw with Fiji. After that disappointing result Gatland went outside his squad and drafted in Cardiff Blues wing Tom James to face the All Blacks.
"I don't know what the problem is with Aled," said Edwards, who is also the Wales Under-20s coach.
"He is the next best left-wing in Wales after Shane Williams. He's a physical specimen and has only just turned 24.
"I would love to see some investment put into him, to see how far it can take him."
Brew grabbed two tries in the derby triumph watched by Gatland, but the wing remains cautious over his chances of making it back into the Wales set-up.
"All I have to do is keep playing well for the Dragons. If it comes, it's a bonus," said Brew.
"Darren has always expressed to us we have to play rugby and it's slowly coming through."
"Things we have been practising on the training field are coming off for us.
"Darren has stressed we're not going to try and simply make the numbers up, we're here to win."
Edwards was equally impressed by his back-row unit of Dan Lydiate, Gavin Thomas and most notably Faletau.
The Tongan-born No.8 has been tipped to win his first cap against the Barbarians at the Millennium Stadium on June 4.
"I would choose all three. People have to open their eyes and see what we have here," said Edwards.
"The boy is unbelievable. He's so dynamic and I think he is going to go far."
The Dragons have three regular season games left to play and if they pick up three wins they could pip the Scarlets to become the third-placed Welsh region and seal Heineken Cup qualification.
The Men of Gwent are next in action in Edinburgh and Edwards is confident his side can continue winning.
"If we play like we did against the Ospreys, we can beat anybody. That's a quality team we've beaten," said Edwards.
"We need to set out to play to win games as opposed to hoping we are going to win games.
"We've done it before and we can do it again.
"I believe in these players. I'm a believer in you've got to make things happen.
"You've got to play rugby to win games. It's the only way we are going to be successful.
"We have some special players and I have total faith in them.
"There is an ambition and desire to do well and, with the stadium upgrade, it's going to be a special future we have here."
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