Chairman Daniel Levy made a £38.5million bid for Argentina forward Aguero and a £35million offer for Villarreal striker Rossi.
Had either bid been successful, Tottenham's transfer record of £16.5million for Luka Modric, would have been smashed.
Harry Redknapp: "Daniel always said that if we found the right player then we would have gone for him but it was difficult.
"He tried something with Rossi. I think he offered £35million in the end.
"It's hard to get top players unless you pay top money.
"You couldn't get Rossi because Villarreal don't want to sell you him."
Newcastle had Rossi on loan from Manchester United in 2006/7. He made only three starts and eight substitute appearances.
He knocked back the chance of further loan deal because he said he was only a "bit player" and did not get the chance to be a first team regular.