Real Sociedad and Valencia are both keen on West Ham's Hernandez.
Newcastle have long been linked with winger Rodrigues.
Scottish Premiership giants Celtic tried and failed to sign Sporting Lisbon right-back Cristiano Piccini before he joined La Liga outfit Valencia.
Reports in France say that Watford are looking to sign Paris Saint-Germain's Goncalo Guedes before Thursday's transfer deadline.
Everton's Henry Onyekuru has been linked to Valencia, despite being on loan at Galatasaray.
Onyekuru was loaned to Galatasaray by Everton this summer.
The 22-year-old was impressive going forward and defensively for Manchester United in their last pre-season clash.
West Ham United were previously linked with Nemanja Maksimovic.
How would a combined Manchester United and Manchester City starting XI look this season?
West Ham are yet to bring in a new signing to the London Stadium this month.
“He calls in the defenders first: breaks a TV. He calls in the midfielders and he breaks a light. Calls in the strikers, breaks a sofa.” One of José Bordalás’s former players tells the tale and, although he’s laughing, he’s only half joking.
Rodrigo Moreno sprinted towards the near post, slotted the ball past Marc-André ter Stegen and ducked behind the goal at the north end of Mestalla, team-mates racing to join the celebrations.
“Every time you looked left and the men in white attacked, you thought: ‘We could lose this,’” said the Valencia coach, Marcelino García Toral.