The French full-back is looking for a way out of the Championship club after two seasons in England.
He impressed early on after arriving in the Premier League, but suffered a season-ending knee ligament injury after just 12 appearances and played no further part in Villa’s slide into the second tier.
He was a regular throughout their 2016-17 campaign and has done enough to draw admiring glances from across Europe.
One offer from the Liga side is understood to have already been turned down, with Villa holding out for a bid of around €10 million.
Sevilla sporting director Oscar Arias is believed to have held positive talks with Amavi and is now looking to do a deal with Villa.
Steve Bruce, who completed a deal for former England captain John Terry on Monday following his release by Chelsea, is prepared to move players on in order to fund additions.
That means that Villa have relaxed a stance which saw them fend off interest in Amavi ahead of the winter transfer window.
Club chairman Tony Xia claimed back in December 2016 that he had turned down a big-money bid for the 23-year-old defender.
He posted on Twitter at the time amid talk of an imminent exit: “Don’t bother reading this. I can tell we have rejected an offer of £25m for @JordanAmavi. He will grow bigger at @AVFCOfficial!”
That is no longer the club’s stance and Sevilla are hoping to tie up a deal quickly now that the summer window is open.