Leicester fell to a fourth-straight Premier League defeat against Manchester United on Sunday, leading to speculation Ranieri's time at the Foxes could be up.
The 3-0 loss at the King Power Stadium saw 18th-placed Foxes move dangerously close to the relegation zone, with Hull now just one point behind.
But Leicester insist they have no plans to sack Ranieri, who guided the Foxes to the Premier League title last season.
Ranieri's side face Swansea on Sunday after tomorrow's FA Cup fourth-round replay with Derby.
And the trip to the Liberty Stadium could prove vital with Paul Clement's men sitting one place behind only on goal difference.
A club statement read: "In light of recent speculation, Leicester City __football Club would like to make absolutely clear its unwavering support for its first team manager, Claudio Ranieri.
"While there is a collective appreciation from everyone at the club that recent form needs to improve, the unprecedented success achieved in recent seasons has been based firmly on stability, togetherness and determination to overcome even the greatest of challenges.
CLUB STATEMENT: #lcfc would like to make absolutely clear its unwavering support for Claudio Ranieri: https://t.co/N4fqYbMlfT pic.twitter.com/CENZOZgCDW
— Leicester City (@LCFC) February 7, 2017
Premier League predicted table: February update
Mon, February 6, 2017Is this how the Premier League table could look at the end of the season (table created by the stats geeks over at footballwebpages.com)
"The entire club is and will remain united behind its manager and behind its players, collectively and firmly focused on the challenges ahead."
Ranieri understands the importance of progressing in the FA Cup and is expected to make a number of changes to his starting XI against local rivals Derby.
The Italian said: "I think (the statement) is for the media. I know the views of the chairman. Maybe he wanted to stop all the speculation. I didn't ask them to do this - I knew what the chairman was thinking.
"Tomorrow is important because we want to go through in the cup. The FA Cup is an important achievement and we have to fight for it. I'll make some changes."