The Toffees were reportedly mulling a double deal for the 21-year-old and Almeria's Brazilian goalkeeper Diego Alves.
On the move? Everton and Palermo have expressed an interest in Piatti (left)
However, the Spanish club's president Alfonso Garcia has indicated he won't sell in January amid a fight to save their La Liga status.
Double swoop: Moyes is also keen on goalkeeper Alves
Almeria sit one place above the relegation zone on goal difference, thanks to Piatti's double in a 3-1 win at Sevilla on Saturday.
The Argentina Under 20 international was plucked from Estudiantes for an undisclosed club record fee - thought to be above £6m - in June 2008.
Almeria's standing means they would find it hard to resist bids for their top scorer, but, with Palermo also keen, they are determined to hold on till at least the summer.
Atletico Madrid and Espanyol have also tracked the 5ft 4in forward, who can play centrally or on the wing and is affectionately known as 'El Duende' - The Imp.
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Source: Daily Mail
Source: Daily Mail