Successive defeats over Easter made it three losses on the spin and seven in the last 11 Championship matches for Pearson's team.
The alarming run, which includes only one win, has seen Leicester go from automatic promotion contenders to slipping two points behind sixth-placed Brighton, who they face at the Amex Stadium on Saturday, in the race for the play-offs.
The Daily Mirror reported on Thursday that Pearson would be sacked before the trip to the south coast.
However, the Foxes boss told reporters ahead of the game: "I am aware of the speculation because people make me aware of it, but the only journey I'll be making is on the team coach with the team to Brighton.
"I have had contact (with the owners). They are good people, they have invested an awful lot in this club - and that's not just finances - and for sure, they will be wanting better results than we have had at the moment.
"But I know that I have their support and that is really all that is important to me. I am in contact with my bosses and I know my own situation and I also know that they have been very supportive throughout the season.
"I don't think there is any need for me to respond to any speculation in the media apart from me to say that all I will be doing is doing everything I can, along with the players, to make sure we finish the season well.
"The important thing is getting back to dealing with what we can affect. We have got to try and distance ourselves from anything external because ultimately, the reason that we are talking about this is because we haven't won enough games.
"If we get back to doing that, then maybe some of the speculation might stop."