Velez Sarsfield are seeking the cash payment, according to the Argentinian side's president Alvaro Balestrini.
Jonas bought out the remainder of his contract with Spanish side Real Mallorca and joined the Magpies on Wednesday in a five-year deal for an undisclosed fee.
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But Velez and Real Mallorca, who each own 50 per cent of the player, both appear unhappy with the 25-year-old's conduct and want more money.
Balestrini claims his club had an agreement with Mallorca the player would return to Velez at the start of this month, but instead he applied to FIFA to become a free agent and signed for Newcastle.
"Jonas should (have) come back to Velez on July 1 because he has a contract with the club," said Balestrini.
He confirmed Velez and Real Mallorca last January turned down an offer from Portsmouth of between eight and ten million euros to acquire the player.
"With this precedent, we are thinking of asking for financial compensation of between four and five million euros to FIFA when he made his request," added Balestrini.
Balestrini is to travel to Spain to discuss the situation with the Mallorca board.
