The France international was strongly linked with a switch to Chelsea in the summer window but remained in Seville after the Blues failed to stump up Sevilla's asking price.
Another scramble for Kounde's services is expected to occur next summer, though, with Real Madrid also rumoured to be in contention for his signature.
However, El Nacional claims that Kounde does not 'trust' Carlo Ancelotti to give him regular game time and has therefore asked his agent to touch base with Man United instead.
The report adds that the Red Devils are 'crazy' about signing Kounde, but Sevilla are not prepared to let the 22-year-old leave for anything less than €90m (£75.9m).
Kounde has featured eight times in all competitions for Sevilla this term and recently became a Nations League winner with France.