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.
Burnley have now received a major update on their pursuit of Sunderland winger Jack Clarke, who they have already submitted a £12m bid for.
What’s the latest Burnley transfer news?
Although they have already spent a total of €91.6m (£78.3m) this summer, the Clarets still have the money to fund a pursuit of a new striker, with Football Insider reporting they are ready to spend £25m to sign a prolific forward before the deadline.
Vincent Kompany believes that adding a new prolific forward to his ranks will be key to his side’s survival in the Premier League, and he is ready to spend big on the right player, having identified some potential options.
FC Nordsjaelland star Ernest Nuamah has recently been named as a target, with it being reported that Burnley are ready to make their move for the youngster, who is valued at £22m by his current club.
However, the Clarets could now be set to face fierce competition for Nuamah, with West Ham United recently submitting a bid, while Tottenham Hotspur and Brighton & Hove Albion are said to be very keen admirers.
Not only is Kompany keen on adding a new striker, he is also running the rule over a new winger, with Football Insider reporting they have already submitted a bid of £10m, rising to £12m in add-ons for Clarke.
However, Sunderland have knocked back that offer, and it has now been reported that the Black Cats have slapped a £15m asking price on their in-demand attacker, who could be tempted by a move to the Premier League.
Despite having their opening bid knocked back, the Clarets retain an active interest in the left-winger, which suggests they could return to the negotiating table with an improved bid, closer to Sunderland’s asking price, before the transfer window slams shut.
How many goals has Jack Clarke scored for Sunderland?
Although he is primarily a winger, the Englishman has managed to find the back of the net fairly regularly for Sunderland, scoring 13 goals in 74 games, during which time he has also weighed in with 18 assists, showcasing his play making abilities.
The York-born winger emerged as a key player for the Black Cats last season, weighing in with nine goals and 12 assists in 45 Championship games, indicating he may now be ready to make the step-up to the Premier League.
Early last season, the Sunderland star also showcased his versatility by starring at left-wing back, receiving praise from journalist James Copley for his performance, who said:
“Two assists of the highest quality and a superb individual goal for Jack Clarke tonight already. All coming from LWB. Not his preferred position coming to Sunderland but my god, what a performance this evening. Just fantastic.”
Although a striker should be a key priority for Kompany, Clarke has proven that he could also be a fantastic addition to his squad, given that he is able to play in several positions, and poses a threat on the front foot, so Burnley should return with an improved offer in the near future.
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