Claudio Ranieri dismissed suggestions Leicester are title favourites after they beat Manchester City on Saturday.
The Foxes' 3-1 win at Etihad Stadium leaves them five points clear of Tottenham, who leapfrogged Manchester City into second place.
Leicester's win prompted bookmakers to cut their title odds, with many making them favourites.
"I don't believe them," said boss Ranieri. "They said I was first to be sacked! But I hope they are right."
The Italian was referring to the reaction to his appointment as Leicester boss in the summer, with bookmakers and pundits giving him little chance of succeeding in his role at the King Power Stadium.
'Fans must continue to dream'
Ranieri, 64, repeatedly played down talk of Leicester finishing the season as champions in his post-match media interviews at Etihad Stadium, saying he did not wish to talk about the title "until the end of April".
"I don't want to think about if we win," he added. "My mind goes over seven days and the next game against Arsenal, a tough match with fantastic players.
"But we are alive and we want to fight. We know it's a crazy league and we have to try. But there are some big teams who have to win.
"We enjoy it and the fans must continue to dream."
All of the other teams in the top five resume their European campaigns this month, with Manchester City and Arsenal in Champions League contention and Tottenham and Manchester United in Europa League action.
All four are also still involved in the FA Cup, while Manchester City are in the League Cup final against Liverpool on 28 February.
And Ranieri conceded the lack of fixture congestion could give his side an advantage.
"We have to think about only the Premier League and how we can fight in it," he said. "Those who play in the other competitions spend a lot of energy and travel a lot and that's not easy. That's a little advantage but we have to concentrate."
|Leicester's remaining fixtures|
|Arsenal (14 February)|
|Norwich (27 Feb)|
|West Brom (1 March)|
|Watford (5 March)|
|Newcastle (14 March)|
|Crystal Palace (19 March)|
|Southampton (2 April)|
|Sunderland (9 April)|
|West Ham (16 April)|
|Swansea (23 April)|
|Man Utd (30 April)|
|Everton (7 May)|
|Chelsea (15 May)|
'We don't feel any pressure'
Leicester were bottom of the table at the same stage of the season 12 months ago.
They had lost four games in a row, were four points behind 19th-placed Burnley and five points from safety.
Ranieri stressed during the first half of this campaign that his team's target was to reach 40 points and safety, and he said the fact they have achieved their pre-season goal means they have nothing to lose.
"I hope my players didn't feel pressure because our pressure was to save the team from relegation," he added. "We did that and now we have to enjoy and do our best, step by step."
Winger Riyad Mahrez - scorer of Leicester's second goal at Etihad Stadium - conceded the victory came as a shock to the Premier League leaders.
"We didn't expect to win here 3-1," said the Algerian, 24. "We're just going to keep dreaming. We're going to fight for the title and see what we can do."