Giuly, 30, is set to leave Catalonia this summer after becoming disilluisoned at his lack of first-team football. Giuly has featured in just eight games this season - his last appearance coming in the 1-0 Champions League win at Liverpool in March.
The Frenchman is available for around £1.5million and is comfortable playing off a central striker or across the midfield. But the Magpies would have to beat off interest from several European heavyhweights with Marseille, Monaco, Fiorentina and Juventus all tracking the player.
His agent Sebastien Riera admitted: "Ludo is aware of Newcastle's interest but no decisions on his future have been made yet."
Bolton's El-Hadji Diouf is a possible alternative target to Giuly for the role of right-sided attacker in Allardyce's favoured 4-3-3 formation.
But with Diouf out of contract next summer at the Reebok, Allardyce may prefer to wait until January to make a cut-price - and hugely controversial - raid on his old club.