The Swans' stunning 2-0 win at Arsenal last weekend has moved them up to seventh in the table, and extended their recent good run to one defeat in 10 games.
Some supporters are even beginning to dream of European qualification, something which seemed unlikely when a poor run in September led to reports of dressing room unrest.
But Norwich are on their own fine run of form and are unbeaten in nine as they pick up steam following a slow start under Chris Hughton.
Davies, 19, says the fact the Canaries have enjoyed a sequence every bit as good as Swansea's means there is no chance of the visitors being under-estimated.
And the Wales international has made it clear the home side's focus is on getting to 40 points as soon as possible, despite their excellent sequence of results.
"The confidence is very high in the group at the moment, and that's just down to the way we're playing," he said.
"Some of the results we've got have been a massive boost, especially after beating West Brom and Arsenal, people are going to start raising their expectations.
"But as a group, our aim is still to reach 40 points and to stay in the league. The earlier we reach that, the further we can try to progress.
"I think it will be a difficult game against Norwich. We won't be taking it lightly and, as long as we can keep it solid at the back, I think we've got the quality up front to get goals."