Southampton are the surprise package of the Premier League this season, conceding just four goals so far and they are sixth in the table.
On Wednesday they go to Sunderland in the Capital One Cup fourth round and boss Mauricio Pochettino is expected to rotate his squad, with Davis expected to replace Artur Boruc.
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 the club's website.
"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 made 11 changes for the last round - a 2-0 win against Bristol City - but they still fielded five internationals.
"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.
"Sunderland have 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."