Saints enjoyed a fairly successful return to the Premier League last term and ultimately finished 14th in the standings. But ambitions on the south coast run much higher than that and last week's decision to pay £8.5million for Lyon defender Dejan Lovren is one indicator of current expectations.
Saints manager Mauricio Pochettino has previously spoken about the possibility of European qualification and Lallana believes they can kick on, telling the club’s official website: "Chelsea at home on New Year's Day is an attractive game so I'm sure the fans will enjoy that one, and we've got Manchester United at home at the end of the season."
He added: "Hopefully we've got something to play for that day and we're in the top half of the table - that's certainly the plan. There are plenty of games to look forward to and I can't wait to start pre-season now."
Southampton will begin the new campaign at West Brom with revenge on their minds, having suffered a 3-0 home defeat last season on the back of a 2-0 loss at the Hawthorns.
"Everyone knows we owe them one after both results last season," Lallana added.
"We've got to settle a few scores but we'll go into those games with open minds and try not to think about that too much. Hopefully we'll get the results we want."
Meanwhile, Southampton striker Billy Sharp denied reports he is set link up with former manager Nigel Adkins at Reading.
The 27-year-old spent last term on loan at Nottingham Forest and it had been suggested he would now move to the Madejski Stadium in a £1.2million deal.
"Don't always believe what u read in newspapers, my loans finished at forest I have 2 years left at saints," Sharp posted on Twitter. "Just for the record I haven't had no medical at reading."