It is believed however that the two clubs are in disagreement regarding the valuation of the player, with Livorno owner Aldo Spinelli determined to hold out for a sum of €10million before parting with the striker.
Paulinho netted 15 times in 35 appearances last season, but the 28-year-old's best efforts were not enough to secure safety for Livorno who were relegated to the second tier of Italian football, finishing bottom of the table in Serie A.
Incoming Southampton manager Ronald Koeman has much work ahead this summer rebuilding a dismantled Saints side, following the sales of key trio Rickie Lambert, Adam Lallana and Luke Shaw.
Southampton were believed to be close to completing the transfer of Pelle last week, but progress in the deal has gone silent meaning Paulinho may be being lined up as a possible alternative.
All may still hinge on Southampton's potential deal for Pelle, but Southampton will need to act fast if they want Paulinho with Udinese and Sampdoria also thought to be in the hunt for the striker's signature.