The Saints are currently sixth in the table, just a point off Manchester United in fifth.
The Saints are on a fine run of form of late, having won five of their last six in the Premier League, the missing win being a 0-0 draw against Arsenal at the Emirates Stadium.
That run has seen them surge up the table, with them currently sitting sixth in the standings and just a point behind Manchester United in fifth.
And Clasie says that finishing fifth in the table is their main aim as they aim to improve upon last season’s seventh-place finish.
“Hopefully we can do it better than last year,” he told saintsfc.co.uk.
“Last year they ended seventh in the table, but hopefully we can climb a bit. Now we are sixth, but we’re looking forward to the fifth position. We’re one point behind Manchester United.
“I think the most important thins is to look to yourself and win your home games and take your points, and then we will see at the of the season where we are.”
A top-six finish is very much up for grabs this season given the Saints' current run of form and the squad that manager Ronald Koeman has at his disposal.
They could even look higher, with Manchester City in fourth just seven points away, a gap that is not impossible to close should they carry on as they have been going in recent weeks.
They are not the only ones eyeing up those places though, with the fights for the title, the top four and the top six all looking likely to go right down to the wire.