Kounde was close to joining Chelsea in the summer before the deal was blocked, and now United are rumoured to be keen to bring him to the Premier League.
Spanish outlet Fichajes report that United are looking to bolster their options and see Kounde as an ideal target to improve their back-four.
Ole Gunnar Solksjaer wants to strengthen the defence that has leaked 17 goals in their last seven games in all competitions. In league competition, United have conceded 17 goals in 11 games this season - which is [at the time of writing] the worst defensive record in the top half of the table.
Harry Maguire is among the United players to have been hit with fierce criticism over his poor form, with the captain reiving his latest round of pelters after scoring in England's 5-0 win over Albania - with legend Roy Keane branding him 'embarrassing'.
The reports in Spain claim the Premier League giants are now considering a move for Kounde and are willing to meet his Sevilla buyout clause of €80m [£68m].
However, it appears they may have to see off competition from former suitors Chelsea, with Thomas Tuchel expected to revive his interest in Kounde as a possible replacement for Antonio Rudiger who would be on his way out of the London club next summer.
Reigning European champions Chelsea reportedly offered £47m for Kounde in the summer window, and it appeared at one point a transfer was imminent.
But Sevilla's director of football, Monchi, pulled the plug at the 11th hour, as the notoriously tough negotiator suddenly decided to stand firm on the 23-year-old Europa League winner's £68m release clause
Kounde came agonisingly close to moving to Stamford Bridge, and recently admitted it affected his start to this campaign.
"Has my failed transfer to Chelsea this summer affected me? Yes, a little bit," said the centre-back.
"But now, it is digested."
Kounde was said to have been angered when his move to Chelsea was blocked in the summer, but he has recovered from this setback.
Sevilla currently sit in third position and a point behind current league leaders Real Sociedad.
Kounde has made 13 appearances in all competitions this season, playing a big part of Sevilla's impressive start to the campaign.