Italian Serie A outfit Udinese are owned by the Pozzo family, who are also in charge of the Hornets, and they are currently in the middle of negotiations which will see Alex Meret and Silvan Widmer move to Napoli.
And it is being claimed that officials will also discuss the possibility of Allan departing the Partenopei and make the switch to the Premier League.
The 26-year-old, who moved to Napoli from Udinese in 2015 for 11.5million euros, scored one goal and made five assists in 39 competitive games last season.
New Hornets boss Marco Silva is keen to bolster the squad this summer after the side finished 17th in the Premier League last term and Allan is thought to be high on his wanted list.
If Udinese can pave the way clear for the player to move to Vicarage Road then Watford can expect to pay 18million euros for his signature given that he still has two years left on his current deal with Napoli.