The Premier League trio are expected to make moves for the Serie A striker this month, with Palermo valuing the player at £31m.
The Argentine is thought to be keen on a move to north London but reports this week have suggested that Arsene Wenger is apprehensive about spending that amount on Dybala.
The Frenchman is believed to prefer a move for PSG striker Edinson Cavani, who has an asking price of just £16m.
However the Italian media have reported that whatever option the Gunners go for, Dybala will not join Manchester United or Liverpool.
Palermo club president Maurizio Zamparini has already spoken about a potential move: “Within two years, he’s going to be better than Cristiano Ronaldo, [Lionel] Messi and [Zlatan] Ibrahimovic.
“It would take €40m (£31m) to take him away from us. He’s the best striker in Serie A.”
By Phil Wellbrook