The 25-year-old moved to Camp Nou from Sevilla in the summer of 2022 and he has since made 88 appearances for the Catalan club across all competitions.
Kounde was a first-team regular under former boss Xavi last season and started 45 of his 48 appearances as either a right-back or central defender.
The France international still has three years remaining on his contract at Barcelona, but reports over a possible summer exit have recently emerged following the arrival of new head coach Hansi Flick.
Indeed, there is speculation surrounding the future of a number of first-team stars at Barcelona, who are under pressure to balance their books amid their well-documented financial concerns.
Kounde, Barcelona ready to part ways this summer
According to FootballTransfers, Kounde is open to leaving Barcelona this summer and the Catalan giants are prepared to sell the defender if they receive a €50m (£42.5m) offer.
The report adds that Manchester United are interested in Kounde, and the player's agility, athleticism, technical skill and versatility is said to appeal to the Red Devils.
Man United have also been linked with Barcelona's Ronald Araujo, Andreas Christensen and Pau Cubarsi this year, although the latter recently committed his future to the La Liga giants by penning a new long-term contract.
Erik ten Hag's side could face competition for the signature of Kounde, as Chelsea, Newcastle United, Inter Milan and Paris Saint-Germain have also been credited with an interest in the defender.
Man United prioritising centre-back signing
Ten Hag revealed at the end of last month that Man United will prioritise the addition of a new central defender, centre-midfielder and centre-forward in the summer transfer window.
New minority shareholder Sir Jim Ratcliffe, who has full control of football operations at Old Trafford, is set to oversee a squad overhaul ahead of the 2024-25 campaign, and a few departures have already been confirmed.
Indeed, Raphael Varane and Anthony Martial are two high-profile players who will be leaving upon the expiration of their contract on June 30, and 36-year-old Jonny Evans could soon follow suit.
The loss of Varane and potentially Evans has increased the need for Man United to recruit at least one new centre-back, and Kounde is one of several targets on Ratcliffe's radar.
It is understood that Everton's Jarrad Branthwaite remains Man United's top defensive target, but his £80m asking price could prove to be a stumbling block.
The likes of Nice's Jean-Clair Todibo, Sporting Lisbon's Goncalo Inacio, Juventus' Gleison Bremer, Crystal Palace's Marc Guehi and Chelsea's Trevoh Chalobah are among a number of other defenders said to be on the Red Devils' list of targets.