Mauricio Pochettino's side have impressed many this campaign and sit sixth after a top-flight start only bettered in the club's history when finishing runners-up in 1983/84.
It is quite a turnaround in fortunes at St Mary's, which only three years ago was hosting third-tier football after falling down the leagues and into financial disarray.
Davis is amongst those that helped Southampton rise through the leagues and will start in goal for them in Wednesday's rearranged Capital One Cup fourth round tie at Sunderland.
The victor will face Chelsea in the quarter-finals and the goalkeeper is relishing the chance to help keep Saints' fine form going.
"We're looking to progress and we know that going to Sunderland, certainly in the position they're in at the minute, will be no easy game," Davis told Saints Player.
"They're certainly looking for a win and they're going to be determined to get the win in any competition, so it's going to be a tough game.
"The fact that the winners will play Chelsea - at this stage - doesn't mean anything.
"We're a determined bunch and we've probably surprised outside of the club along the way this season.
"We're looking to enhance the position that we're in and progress in every competition.
"If you're going to build a team and a club that's going to be successful then that's got to be our mentality.
"We've certainly had that over the last few seasons and we want to continue it."
Pochettino is expected to ring the changes at the Stadium of Light, having made 11 alterations for the 2-0 win against Bristol City in the third round.
That side still included five senior internationals and highlights the strength in depth at the Argentinian's disposal.
"We've got a strong squad and an ambitious group of players which the manager and the chairman have put together, and we're all looking to play as many games as we can to progress," Davis said.
"I think there's a genuine desire amongst all the lads to be in the first team and I think, with the results putting us in a different position, we're pushing all the time.
"I speak for myself and the other lads that get their chance in this competition that of course you want to do well and show the manager if any changes are needed then you're ready and you're prepared to wait for your opportunity.
"If you stay professional, then it's an opportunity for everyone who steps out on the pitch on Wednesday to do that."
Southampton are favourites with the bookmakers to win the fourth-round clash, which sees Davis line up against his former club.
The 37-year-old endured a tough year at Sunderland and left for St Mary's following relegation from the Premier League in 2006.
"It wasn't a successful period in my career, but I certainly look back on it as a learning period in my career," Davis said.
"There are things that I learned while I was there that I use today and obviously make you stronger and give you different experiences.
"It's a fantastic club and a fantastic stadium, and when things are going well there everything goes well - but, likewise, when it's not going so well it can go the other way, and that's a certain situation for them at the moment that affects them.
"They've changed their manager and they're certainly in a difficult period at the moment, but it's of no interest to me as we're just looking to progress into the next round of the cup."
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