The Saints have made their ambition clear their summer, sanctioning several big-money signings.
A club record deal for Italian striker Pablo Osvaldo has taken their spending spree past the £35million mark and has helped to raise expectations on the south coast.
Lovren is among those to have been drafted in by Mauricio Pochettino to help take Southampton to the next level, and he believes rapid progress could be on the cards.
He said in the Daily Mirror: "Every player here thinks we can get into the Champions League within the next two years. It is a big job, but everything is possible.
"Playing in the Champions League is an experience you can never forget and I hope to do it with Southampton.
"We can do something big this season. I want a place in the top seven or eight."
Lovren opted to join Southampton from Lyon over a number of other English sides, and he is convinced he has made the right decision.
He added: "Southampton is a big club, because I see everything here. I see the organisation and every deal. We do things like the big clubs.
"It was not an easy decision to leave Lyon, but after a discussion with the chairman and the manager it was an easy decision.
"I love to be part of this project and Southampton really wanted me. It was important for me to know that.
"English fans love football, they have passion - it is not the same in France. It really is something special here."