The Serie A outfit are aiming to clear the decks during this month's transfer window with Baronio a likely departure.
Baronio has incurred the wrath of Perugia's outspoken president Luciano Gaucci and does not have a future at Renato Curi.
The midfielder only joined Perugia at the start of the season but is on the shopping lists of Napoli and Torino.
Experienced striker Amoruso (pictured) is another heading for the exit door and he has repeatedly been linked with a move to The Premiership.
West Ham have previously been mooted as suitors of the former Juventus marksman and could renew their interest given their pressing need for striking reinforcements.
But Everton and Birmingham are unlikely to rekindle their interest having landed Brian McBride and Christophe Dugarry respectively while Piacenza are also keen.
Perugia's Serie A rivals Brescia are eyeing a swoop for 28-year-old defender Viali, who has been unable to nail down a regular starting place.
As replacements, Perugia want to take Milan's teenage stopper Mohamud Sarr on loan but are likely to be rebuffed by Sampdoria in a bid for striker Fabio Bazzani.
