The Jaguares forward was expected to join Tottenham this summer, but the move fell through earlier this month.
Palace have invited the 20-year-old to join them for pre-season training and he featured in Tuesday's friendly at Wycombe.
Freedman will have another look at Pedroza in Friday's clash with Crawley before deciding whether or not to pursue his interest.
"There is compensation involved for Antonio but the deal is doable," Freedman told the South London Press. "I can't quote you how much but everything checks out.
"He will be available for the Crawley game. I was after the kid in the summer but I was let down by someone and he ended up going to Tottenham. But they decided not to do the deal for whatever reason.
"He's a young kid and we'll keep him here and see how he goes."
Palace have also taken French defender Francois Marque on trial with the 27-year-old playing in the draw with Wycombe.
"Francois has a decent pedigree and we're going to have a look," added Freedman. "I don't want to get 100 trialists in - only in positions where I'm realistically going to sign players.
"There is no secret there is not millions to spend so I'm going to have to dabble about. I won't sign anyone I don't think will push us on.
"They have to have the potential to make us better or make the club financially stronger by possibly being able to be sold on."
Source: Team Talk
Source: Team Talk