Rodriguez was an unused substitute as England defeated Denmark at Wembley on Wednesday, with team-mates Luke Shaw and Adam Lallana both playing some part, while Schneiderlin is yet to make a senior appearance for France.
However, the former scored the only goal as Southampton won 1-0 at Crystal Palace in the Premier League on Saturday, and Pochettino is certain his striker could make a big impression in Brazil.
"I think the goal showed exactly what Jay Rodriguez is made of," he said. "It showed his quality, his speed, how brave he is and his technique.
"I think he has the talent and the skill to go with the English national side and to play for the national side.
"I think his call-up to the side by Roy Hodgson was fully deserved, and to win your place you need to deserve your place to be going to the tournament.
"By scoring goals as he did today, he's definitely increasing his chances."
Pochettino also called on France coach Didier Deschamps to make a trip to England to take cast his eye over the as-yet overlooked Schneiderlin.
"Until the final list is given, I think he has his chances," he added. "I would actually invite the France national manager to come and see him direct, because I think he has the skill and the quality to play with the France side.
"Hopefully that will happen. I would be very pleased for him if that does happen."
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