Bale announced his retirement on Monday, bringing an end to a glittering career that saw him become Wales' most-capped male player and record men's goalscorer.
He walks away from the sport as one of Britain's most decorated players, having won five Champions League and three LaLiga titles with Real Madrid after playing six seasons in the Premier League for Tottenham Hotspur.
"When you've got somebody like Gareth Bale and what he's done for Wales and the impact he can have even in the changing room... then you know I've got to take advantage of that and he's interested to do it in whatever capacity," Page told reporters on a Zoom call on Tuesday.
"That's something we'll have a chat about further down the line in the next couple of weeks and something that I'm passionate about and want to keep him involved.
"I think he will be interested, absolutely. There might have already been discussions before this about staying involved in some capacity."
Page said Bale informed him on Sunday that he was hanging up his boots before he made the announcement on social media.
"He told me that he was retiring from football completely, which did come as a surprise at that moment in time and I wasn't expecting that from him in that phone call," Page said.
"But when you take a step back, strip your emotions out of it, I get it, I understand why he's done and for him to finish at the top of his game. I completely understand it."
Bale helped Wales qualify for the 2022 World Cup, ending a 64-year wait to reach the finals again. The talisman also played a key role at the 2016 and 2020 European Championships.
Page described Bale's career as "phenomenal".
"He has put Wales on the map globally because of what he has done in European football with Madrid, in the Premier League with Tottenham and then in the World Cup," he added.
"He will be missed and it's not the news that we wanted to start the year, but we all knew it was going to come up one day."
