Leicester's unlikely surge to the summit has forced the Italian coach to revise expectations having previously stuck to his mantra of needing 40 points to secure survival.
The Midlands club, who avoided relegation by six points last season before stunning everyone with their brilliant form in the first half of the current campaign, passed the 40-point milestone at the start of January.
After a 1-1 draw at Aston Villa on Saturday put them a point clear of Arsenal at the top of the table, Ranieri said the target for the remainder of the campaign, was to improve on the 39 points they took in the first 19 games of the season.
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"Our next target is 40 more points from the second half. I know it is very difficult and ambitious but why not?," the former Chelsea coach told the BBC.
The Premier League has only been won with 79 points or fewer on three occasions, but no team has finished outside the top four with that total.
Manchester United won the title in 1997 with 75 points and again in 1999 with 79 points, while Arsenal won it in 1998 with 78 points.
Saturday's draw at bottom club Villa was tinged with disappointment for Ranieri.
His side took the lead through Shinji Okazaki but Riyad Mahrez missed a penalty and they were then pegged back when Rudy Gestede netted for the hosts in the 76th minute.
"We had the match in our hands but that is football... a point is OK," the Italian said.
(Reporting by Toby Davis; editing by Patrick Johnston)
