Manager Pearson confirmed talks have progressed with the former Inter Milan midfielder, who is available on a free transfer.
The ex-Argentina international could be in before Leicester host Arsenal in the Barclays Premier League on Sunday ahead of Monday's transfer deadline.
He is available after leaving Inter following 10 years at the San Siro and Pearson remains upbeat over the deal.
Pearson said: "Cambiasso is still a possibility
There's been progress over the weekend so I'm more hopeful than I was on Friday and Saturday but until there is a definitive answer I'm loath to talk too much
But I am hopeful it can be done in the next couple of days.
"We've been trying to do business and it has not materialised so far
But hopefully this week we can still do business and bring players in that we want to bring in.
"I recognise there is a need for added numbers and we have to do that in this window
There are subtle differences this year to last year.
"We've been very positive but it is nice to have different options.
"Two or three hopefully is the aim
It would be nice to be able to achieve that."
Leicester host Shrewsbury, where Pearson started his career, in the Capital One Cup on Tuesday without Danny Drinkwater (hamstring), Jamie Vardy (thigh) and Matty James (shin).
Pearson added: "Danny will be introduced back into training this week so may be available for the week
Matty's shin is still sore so we will have to take that one at the right pace especially with a break coming up."
Source : PA
Source: PA