Negredo, 22, was in splendid form for the Spanish club, netting 13 goals in 36 impressive appearances that saw Almeria propel to 8th in La Liga.
Newcastle United's Technical Coordinator Jeff Vetere, who had nurtured the youth in his Real Madrid days, is said to be manufacturing the move for the English club.
It is understood that Real Madrid have a £3m first option on the their locally born 22-year-old, with reports suggesting they are keen to exercise this, and then sell the player to Newcastle for a profit.
The Sun suggests that the fee could be in the region of £9.5m, and that Magpies boss Kevin Keegan is keen to wrap up the deal in the coming weeks.
However, with Tottenham Hotspur also interested in Negredo, the Toon Army may have their work cut, considering they lost out to the Londoners in deals for defender Jonathan Woodgate, and Croat Luka Modric earlier this year.
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