The Saints are currently second on the league table after six matches and although new boss Koeman knows that type of form will be difficult to keep up all season, he is looking to produce a more successful campaign than the likes of Tottenham and Manchester United who are placed eighth and seventh respectively.
"If we continue like this, there is a possibility but normally teams like Tottenham, Manchester United will be up [in the table] because they have enough very good players," he said on Friday ahead of Sunday's trip to Spurs.
"That makes the club big, the name is big, but we try to do it our way. If we keep the belief and keep the spirit nothing is impossible.
"It was a difficult start to the season with all the changes in the team. We're enjoying very much our start.
"It's a long season but we know our qualities. The most important thing is to keep the spirit and our way of playing. What we showed [in the 2-1 defeat] against Liverpool is the example of how we have to play."
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