The 22-year-old is a sought-after prospect after impressing with the La Liga club and playing a big part in their Europa League triumph last season.
According to El Gol Digital, Arsenal and United are interested in the France Under-21 international and could sign him for a cut-price fee in the summer.
Kounde is valued at €90 million (£77m) by the Spanish club, but they could be willing to lower their demands to reach an agreement with one of the English suitors.
The Red Devils ended their pursuit of the centre-back when they were alerted to his price tag and started looking at Villarreal’s Pau Lopez instead.
But the Old Trafford club revived interest after Sevilla decided to reduce their demands by more than 30 per cent to €60m (£51m).
That news also caught the attention of Arsenal, who could be set for a transfer battle with their Premier League rivals at the end of the season for the youngster.
And it came after Sevilla rejected a €55m (£47m) bid from Manchester City for the player a few days ago, a figure that was considered too low.
Kounde has scored three goals in 38 appearances for Sevilla this season in all competitions, helping his side to fourth place in La Liga.
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