Veretout, 22, enjoyed a breakout season at Nantes last term in a playmaking role, recording seven goals and seven assists in 36 Ligue 1 games as the club secured a 14th-place finish.
His impressive performances did not unnoticed across the Channel either and a number of Premier League clubs have since been linked with the former France Under-21 international’s signature.
Ouest France's report names both Liverpool and Tottenham Hotspur as rival suitors but follows up Le Parisien's earlier claims that Villa have now raced to the front of the queue and are closing in on a deal.
The suggested fee would also be quite a coup considering a previous report from L’Equipe claimed that Tottenham had lodged a bid of around €15 million [£10.6 million] – news that drew a revealing response from Nantes chairman Waldemar Kita at the time.
Admitting that the club would have to sell Veretout, whose current contract expires in 2017, if he demanded a wage increase in the near future, Kita told L’Equipe: "That would really piss me off.
"The problem is that there is a tax in France that does not exist elsewhere. If he has a delusional salary, he comes to see me and he decides to leave, it will be difficult to oppose. I will not have a choice.
"I can just kiss him and wish him good luck.
"We cannot always be selfish, protectionist and paternalistic. Jordan has a career to manage. I will not stop his footballing and economic development."
A versatile prospect, Veretout operated in a No. 10 role for a good chunk of last season but also impressed in a two-man central midfield whenever Nantes manager Michel Der Zakarian switched to a 4-4-2 formation.
Those all-round skills would be a more than welcome addition to a Villa squad which lost skipper Fabian Delph to Manchester City earlier this month, leaving new boy Idrissa Gueye, Ashley Westwood, Carlos Sanchez and Gary Gardner as the only other middle men at manager Tim Sherwood’s disposal.
His potential arrival would also make him the club's fourth summer signing from Ligue 1, with Gueye, left-back Jordan Amavi and striker Jordan Ayew all joining from Lille, Nice and Lorient, respectively, in recent weeks for a combined £28 million.
At this rate, it won't be long before French is the dominant language in the claret and blue dressing room.