Defence coach Shaun Edwards and forwards coach Robin McBryde are out of contract at the end of the World Cup.
And attack coach Rob Howley's deal will expire after next summer's tour.
Given Gatland is under contract until the 2019 World Cup, Davies said he "may well look to see if there's a need to renew the coaching set-up".
Head coach Gatland and his assistants have worked together since 2008, winning three Six Nations titles, including two Grand Slams, and fly-half Dan Biggar has said it is vital they remain in place.
Having reached the World Cup semi-final in 2011, they were knocked out at the quarter-final stage this time by a 23-19 loss to South Africa.
Davies said he and Gatland will now evaluate the performances, which included a win over England in the pool stage, and discuss what happens next.
"We'll have a conversation to see how everything went in the competition," Davies said.
"It's not just when you fail to get out of the group that needs to be done, like all the focus has been on England.
"There needs to be a review on how we can improve moving forward."
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The Rugby Football Union has begun its inquest into England's disappointing World Cup campaign, which ended at the pool stage following defeats to Wales and Australia at Twickenham.
If the report's conclusion is to sack head coach Stuart Lancaster, reports suggest England may attempt to tempt Gatland away from Wales.
Edwards, who has moulded Wales into one of the world's best defensive outfits, could also be courted by England, especially given his immediate availability.
Gatland's worth to Wales was highlighted in December 2013 when he was given a contract extension until 2019 and Davies fully expects him to see it through.
"I think he's done some really good work to be perfectly honest," Davies added.
"If you look at all the difficulties we've had in this competition... the fact is that we've performed better than the expectation, when you consider all the injuries we've had.
"So as I said, Warren has a contract that lasts another four years so it's up to him to assess who he wants for Wales.
"I'm not really interested in all this talk in the papers of who wants him, because that fact is he's under contract with the Welsh Rugby Union."
Warren Gatland will be the one to decide whether changes are needed to his coaching team, according to Welsh Rugby Union chairman Gareth Davies.