The 22-year-old has emerged as a potential option to play a back-up role to Barca left-back Jordi Alba, with manager Luis Enrique keen to complete a deal in the near future.
Reds boss Jurgen Klopp is thought to be looking to sign another another full-back in order to provide under-fire star Alberto Moreno with more competition following criticism for his performance in the Europa League final defeat to Sevilla.
Aside from Guerreiro, Klopp is also considering a possible deal to sign Leicester City’s Ben Chilwell as he plans for a summer overhaul.
The same goes for the Gunners as manager Arsene Wenger looks to bring in another defender pending the potential departure of Kieran Gibbs given his very limited playing time.
It is believed that Guerreiro is worth around the £9m region, with Barcelona, Liverpool and Arsenal all all mentioned by Sport as potential suitors.
He made 41 appearances in all competitions for his side last term, scoring a total of three goals while providing another two assists.