The 27-year-old enjoyed a fine season at the Mestalla Stadium during the recently concluded campaign, netting 16 times in La Liga alongside providing four assists, while also scoring three in the Copa del Rey.
The frontman's showings were enough to attract the attention of Spain boss Julen Lopetegui ahead of his side's trip to Russia for the World Cup - with the Brazil-born attacker named as part of La Roja's travelling contingent.
However, according to the Sun's Alan Nixon, Rodrigo has also peaked the interest of both Arsenal and Chelsea, and the Europa League pairing are keen on securing the talisman's services.
Both sides struggled for goals during the 2017/18 term, with the Blues' lack of firepower up top particularly a significant factor in them missing out on Champions League football next year.
The Gunners certainly became more prolific following the big-money signing of Pierre-Emerick Aubameyang from Borussia Dortmund in January, yet Alexandre Lacazette's slow take to English top flight football appeared a concern.
However, one obstacle that the Premier League duo may fail to overcome is the offering of top tier European football, with Valencia's fourth-place finish securing them a spot in the continent's most glamorous club competition.
Another aspect is the player's reported desire to remain at the Mestalla for at least another year, with Spanish news outlet Don Balon claiming Rodrigo has shown no interest in Chelsea or Atletico Madrid and Paris Saint-Germain - two other European giants who have also been linked.