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The 23-year-old is yet to make a first team appearance for the Red Devils, since arriving at the club from Czech side FC Slovácko.
He has gained first team experience on three loan spells, two in League One with Swindon Town and Burton Albion and another last season with Sparta Prague in the Czech First League.
According to Czech publication Idnez Villa have seen enough to be interested in signing the goalkeeper, wanting to bring him in as back-up to Emiliano Martinez and second choice stopper Robin Olsen.
The report states that Manchester United are hoping to get at least £6m for Kovar, an asking price which has put off Sparta Prague and other interested parties in Germany.
Kovar has already featured for Manchester United during pre-season, impressing in the 1-0 win over Lyon and playing half the win over Leeds.
He was left out of the summer trip to America, with new goalkeeper Andre Onana arriving and had been expected to move on loan again this season.
However, a permanent move could now be on the cards with Aston Villa liking what they have seen from the Czech Republic Under-21 international.
Villa have already signed Pau Torres from Villarreal, Moussa Diaby from Bayer Leverkusen and Youri Tielemans from Leicester so far this summer.
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