Robert Page's side must get past Finland in Cardiff and either Poland or Estonia on March 26th to qualify for the tournament.
They will be favourites to beat Finland, although Tottenham Hotspur defender Davies says it is a tricky test.
Former Arsenal player Ramsey, who is usually the Welsh captain, has only just returned from injury and has hardly played for Cardiff City, so his involvement will likely be limited to a place among the substitutes.
"The opportunity to have Aaron in this squad is a no-brainer," Davies said on Wednesday.
"On his day, he can flip a game on its head, produce a moment of magic.
"We're lucky to have him."
Wales stalwart Davies believes Finland must not be taken lightly.
"They had a good qualifying campaign. They've got a well-organised team and players who can hurt you if you're not switched on," he told reporters.
"We're anticipating a tight, nitty-gritty game because of how well-organised they are."
Wales have twice lost at home to Finland, once in a friendly and in a World Cup qualifier in 2009.
Their last meeting was in 2021 when a friendly ended 0-0.
"They're here for a reason. They're a good outfit," Page said. "We've played them in the Nations League and friendlies recently. They're going to be a big physical team and they'll pose a threat. We're going to have to be at it.
"If we play as well as I know we can, the result will take care of itself."
Page's inclusion of Ramsey in the squad was seen as something of a surprise, but Page says he brings something invaluable to the younger players in the squad.
"To have people like Aaron, who has that ability even if he doesn't have the legs he used to have, is great for the younger players," he said.
"That experience will have an influence on the group."
