Claudio Ranieri has challenged Leicester to pick up even more points in the second half of the season than they managed in the first, but still refused to talk about winning the title.
The Foxes are second in the Barclays Premier League and are just a point away from Ranieri's pre-season target.
The Italian wanted 40 points to guarantee survival and victory at home to Bournemouth on Saturday would see them past that mark.
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Ranieri admitted he did not expect to reach his goal so soon but now wants his men to eclipse it in the second half of the season.
He said: "We'll try to do the same - as we've achieved 39 points then we'd like to achieve 40 points - one point more. I will be satisfied.
"Nobody can take our 39 points and we want to improve. We have a job to do because we make a lot of mistakes and we have to improve a lot.
"A success is maintaining the Premier League (status) but it is how we achieve the next 39 points."
Leicester are behind Arsenal on goal difference after Tuesday's 0-0 draw with Manchester City and have only lost twice in the league this season following Saturday's 1-0 defeat to Liverpool.
But Ranieri, who is set to pick from an unchanged squad, dismissed any further talk about a title tilt.
He said: "You would love it if I said 'we are champions'. No, I say 'we want to beat Bournemouth'.
"At the beginning of last season we were only talking about relegation, this season it's top of the league. It's important to maintain the right balance.
"We can say 'start to win the title' but it's not our job, our job is to win the next match. The other (clubs') jobs are to win the title. We have to fight for the next match and we want to win. That's our philosophy."