Speroni has been an ever-present for Palace this season following their promotion to the Premier League, and Jedinak believes that Argentina coach Alejandro Sabella should include him in his plans for the finals in Brazil.
Jedinak, who will also be at the tournament with Australia, praised the 34-year-old for his eight clean sheets in the league and said that he would love to see Speroni's form rewarded with a first international call-up.
"He doesn't get called upon but when he needs to, he's there," Jedinak told the Croydon Advertiser. "That's how you know he's a top goalkeeper.
"He's quiet and then all of a sudden gets called into work. Having that concentration is required and I think Jules knows that - he's been doing that for a long time for Crystal Palace and he will keep doing that.
"I would love to see him at the World Cup. I would love to see a very fine gentlemen's dream come true. It would be extra special because it's something I have experienced myself.
"For Jules, it would be something that would mean an awful lot to him."
Argentina begin their quest for a third World Cup with group matches against Bosnia-Herzegovina, Iran and Nigeria.
