The Saints made a slow start to the campaign, but they have put tighter a strong run of form at the right time.
Southampton have won four of their last five matches to move up to sixth place in the Premier League standings, and Koeman is hoping that his side can go on to claim a spot in Europe.
"Of course we have some objectives before the season," Koeman said. "What we did last season meant we got an opportunity to play in Europe - and that's our ambition.
Southampton’s recent surge up the table has been coincided with the return of goalkeeper Fraser Forster from injury.
The former Celtic stopper has missed much of the campaign so far, but he has returned in wonderful form.
Southampton have not conceded a goal in any of the six matches that Forster has played this season, and the England international custodian appears to have made their defence much more confident.
Forster can actually equal a club record for consecutive clean-sheets in the Premier League if he is able to to stop Chelsea scoring in the Saints’ next match.
Paul Jones is the current holder of the record, having achieved the feat of keeping seven clean-sheets in a row back in 2001.