Dybala is at the end of his deal with Juventus in the summer and is currently scheduled to depart as a free agent, with no agreement over fresh terms.
He has already been linked with a host of clubs, including Tottenham Hotspur and Liverpool, and now, according to Italian daily Corriere dello Sport, Arsenal and Newcastle are keen.
Dybala represents an attractive free agent possibility for Arsenal, who will hope to have Champions League football next season, and Newcastle as they aim to kick on with their project.
At present though Dybala would prefer to remain within Serie A.
He has interest from Inter, while AC Milan are also a possible destination for the Argentine.
The 28-year-old has scored eight times in 22 Serie A games for Juventus this season, along with striking on three occasions in the Champions League.
In Europe, Dybala has never played his club football outside of Italy and it remains to be seen if that will change in the summer.
