The Senegal international joined the Catalan giants from K.A.S Eupen back in 2018 but has failed to make the grade in La Liga.
The 21-year-old was promoted to the first-team under former manager Ernesto Valverde, yet his struggles saw him sent out on loan to Ligue 1 side OGC Nice for the second half of the season.
With his future in Catalonia seemingly up in the air, Spanish outlet Mundo Deportivo (via Sports Witness) report that the Hammers remain very keen to sign the player and are one of the clubs to have shown the 'most interest'.
The young full back has previously been linked with a move to the London Stadium following the club's failure to tie promising defender Jeremy Ngakia down to a new contract.
With Ngakia now having having left the club following the expiry of his deal - and with veteran defender Pablo Zabaleta also departing in June - the club is in desperate need of reinforcements on the right side of defence.
Wagué may have been limited to just six appearances in all competitions during his time at Barça, but he has valuable experience at international level, having played at the 2018 World Cup and the Africa Cup of Nations in 2019.
The report also suggests the player is potentially close to securing a transfer, although it is unclear if that deal would see the player moving to the Hammers.
As for Barcelona, they have already been linked with a number of right back options, with current full back Nelson Semedo expected to depart the club. One name that has bizarrely been rumoured for a move to Camp Nou is Manchester United's Diogo Dalot, who Barça have previously tried to sign.