Pearson's future has been called into the question with Leicester bottom of the Premier League table following a dreadful run in which they have taken only two points from their last 12 games.
The former Hull City boss guided the Midlands club to the Championship title last season and Leicester legend Walsh wants Pearson to be given time as well as funds in the January transfer window to turn the club's fortunes around.
Walsh believes Leicester's owners will stick with Pearson, but the former centre-back knows results must improve soon or they may opt for a change.
When asked if Pearson is the right man for Leicester, Walsh told Perform: "I do believe he is, yes, and I don't see the point in changing.
"I don't think the owners are going to do that at this moment, but the more it goes on the more difficult position for Nigel it becomes.
"The pressure is high now on Nigel Pearson, there is no doubt about it. I'd like to think that maybe in the window he got some money to spend, which I'm sure he will have.
"He knows himself he needs to buy a couple of players of the right calibre to deal with the position that Leicester are in.
"It's not going to be a big attraction for a lot of the top players anymore, because of the position that we're in."
Walsh stressed the importance of Leicester cutting out the errors and being more clinical in front of goal if they are to get out of trouble.
He said: "We are obviously going wrong somewhere and I think that is making silly mistakes, which we shouldn't be doing and it's consistently bad, so that has to stop.
"And also at crucial times of the game we have had good chances and not put them away and that would make a big difference. The difference is that these top-class strikers and players put chances away and we've not been doing that.
"We have had a foothold in games and just not got that goal which would have changed the game."
Leicester face Tottenham at home on Boxing Day before a trip to fellow strugglers Hull City two days later.
