Veretout has struggled to live up his eight-figure price tag
Villa fought off interest from Leicester City to land Veretout in a £10 million deal from Nantes a year ago, but the Frenchman was one of several to disappoint as the Villans fell into the Championship with little resistance.
Despite this, the report claims that Veretout, who hasn't played a single minute of first team football since Remi Garde was sacked in March, is wanted by clubs in England, France and throughout the continent - although he is deemed more likely to move abroad if his spell at Villa Park is brought to a premature end.
Moments like these have been few and far between for Veretout
Di Matteo's appointment was confirmed by Villa at the start of this month, and the Italian has already been linked with a host of fresh faces as he looks to build a side capable of returning to the Premier League.
HITC understands a reunion with Graham Dorrans, who scored 13 goals for Di Matteo's West Brom side en route to promotion in 2009-10, could be on the cards, while there is also interest from Villa in former Manchester United's Nick Powell.
Norwich man Dorrans is being tipped for Villa Park
Talks between Veretout and Di Matteo are expected to take place later this month, the report claims.
New boss Di Matteo is a Champions League winner