The talented 22-year-old has been linked with a move to the Premier League this summer and, following Fabian Delph's controversial departure to Manchester City this month, Tim Sherwood has stepped up his chase in recent weeks.
Villa have reportedly agreed a fee in the region of £10.4m for the France Under-21s star but Liverpool and Spurs are monitoring the situation and are ready to strike if talks break down.
Nantes president Waldemar Kita has since told Parisian newspaper L'Equipe that a deal has been 'basically agreed' with an English club.
"We are basically agreed on everything," Kita said. "I am obliged to give in, he is 22, he has a big future and he will play for a great English club."
Villa recently confirmed the £8.5m capture of Jordan Ayew, brother of Swansea's Andre, from Lorient days after securing the services of defender Jordan Amavi from Nice for £10m.
At the beginning of the summer transfer window, Sherwood also lured former Manchester City right-back Micah Richards to the Midlands following a campaign which saw the Villains scrap for Premier League survival once more.
Meanwhile, Nantes president Kita has complained the tax rate for high-earners in France has a part to play in Veretout's decision to leave the club.
"The problem is that there is a substantial tax in France that does not exist elsewhere," Kita said. "If (Veretout) has a delusional salary and he comes to see me and decides to leave, it will be hard to oppose."
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