Morgan Schneiderlin says Southampton can "shock the world" and qualify for the Champions League this season.
The midfielder, 25, believes Saints, currently third in the Premier League, can stay in the top four as "something special is going on" at the club.
"We want to put Southampton in the spotlight. That will be a shock for the country and the world," he said.
"We want to reach the Champions League. We want to change this tradition of it being all the big teams."
Schneiderlin says the Southampton dressing room is focused on maintaining their excellent form, which has brought 39 points from 21 games and, most recently, a 1-0 win over Manchester United at Old Trafford on Sunday.
"Before every game, we say 'Lads, we cannot let this slip away,'" the Frenchman revealed.
"We have to make it happen and to make it happen we need to be focused in every game, to not get 'big time'.
"We are Southampton. We are players like myself who four years ago was playing in League One. Never forget where you have come from.
"Hopefully we can do something special. We are believing we can but if we don't, the most important thing is to get Europe for Southampton."
Schneiderlin's own future has been the subject of much speculation after he criticised the club last summer when Calum Chambers, Adam Lallana, Rickie Lambert, Dejan Lovren and Luke Shaw were all sold.
Reports have linked Schneiderlin with moves to Manchester United and Arsenal and he says he "can't say what's going to happen in the summer".
He added: "That's up to everyone's personal choices and the club choice. We are going to see where we are going to finish and what everyone's going to do but right now I can't predict anything."
Meanwhile, Southampton will be without Toby Alderweireld for Wednesday's FA Cup third-round replay against Ipswich at Portman Road after the defender was ruled out for up to four weeks by a hamstring strain.
Alderweireld was taken off in the first half at Old Trafford on Sunday after picking up the injury.