Estudiantes signed the winger on a free transfer from River Plate last summer and he has scored 13 times in 65 appearances for the club.
He has been heavily linked with a move to the Premier League this summer with several clubs believed to be interested in him.
Newcastle have been keeping tabs on Rollheiser, but at least two more Premier League clubs have shown an interest in him.
Burnley and Sheffield United are amongst the teams who have been made aware of the deal conditions for the Argentinian winger.
It has been claimed that the two Premier League clubs are aware of his price and his availability.
But Rollheiser is now close to agreeing on a move to join Russian side Zenit in the ongoing window.
A fee is close to getting agreed upon and the offer from Zenit are claimed to be too big for the player to reject.
