Press Association Sport understands the player is discussing terms with the Magpies with a view to completing a £5million switch to St James' Park.
Newcastle have been targeting the 27-year-old Spaniard, as well as Arsenal's Lucas Perez, in recent weeks as Benitez attempts to add firepower to his team.
Joselu, a £5.75million signing from Hannover in June 2015, scored only four goals in 27 appearances during his first season at Stoke, and spent the last campaign on loan at Deportivo la Coruna, where he managed six in 24 run-outs.
Benitez has repeatedly expressed his frustration in recent weeks at the club's relative lack of transfer activity and with owner Mike Ashley having made it clear that he will not break the bank, he is having to be inventive in the transfer market as he waits to offload players now surplus to requirements in the top flight.
He saw his side lose 2-0 at home to Tottenham on their return to the Premier League on Sunday with Dwight Gayle operating as a lone frontman and only Aleksandar Mitrovic as back-up on the bench.