The 24-year-old has made an impressive start to the 2021-22 campaign, scoring five times and registering one assist in eight appearances for his Portuguese outfit.
Meanwhile, the attacker has found the back of the net on 30 occasions in 105 outings for Porto since arriving in July 2019, in addition to contributing 14 assists.
Tottenham Hotspur and Chelsea were both linked with the Colombia international over the summer, with Diaz's agents believed to have travelled to England for informal talks.
According to El Nacional, Barcelona are now firmly in the race for the left-sided attacker, and the Catalan outfit are keen to complete a deal during next summer's transfer window.
Diaz has scored five times and registered one assist in seven league appearances this season, while he helped his side claim a goalless draw against Atletico Madrid in the Champions League on September 15.
Monaco 
Stade Brestois 29 
Bordeaux 
Nimes 
Bayern Munich 
FC Augsburg 
Paris Saint Germain 
Toulouse 
CSKA Moscow 
FC Rostov 
Leicester 
Chelsea 
Valencia 
Betis 
Dynamo Kyiv 
Chornomorets Odesa 
Verona 
Inter 
Bayer Leverkusen 
FC Heidenheim 
Borussia Dortmund 
SC Freiburg 
VFL Wolfsburg 
Union Berlin 
Arsenal 
Nottingham Forest 
Everton 
Brentford 
Spartak Moscow 
Lokomotiv Moscow 
Rangers 
Dundee Utd 
Atletico Madrid 
Alaves 
Lens 
Marseille 
Ingulets Petrove 
Shakhtar Donetsk 
AC Milan 
Juventus 
ST Malo 
Manchester City 
Tottenham 
Eintracht Frankfurt 
Werder Bremen 
Girona 
Espanyol 
Feyenoord 
Heerenveen 
ST Etienne 
Montpellier 
Grenoble Foot 38 
Heart Of Midlothian 
Celtic 
Reims 
Lyon 
PSV 
Groningen