Clark has become a target of West Bromwich Albion, who are reportedly prepared to offer £4.5 million for his services.
Villa appear set to reject that offer from their Midlands rivals - as they are determined to keep hold of Clark.
The Claret and Blues are looking to trim their wage bill, following their relegation to the Championship.
However, Villa do not want to lose Clark - who they believe could have a key role to play next term.
Di Matteo has been impressed by Clark’s performances over pre-season, and would rather raise funds by selling other members of his first-team squad.
Villa are expected to part ways with the likes of Idrissa Gueye and Jordan Veretout before the close of the transfer window.
Villa’s competitive season gets underway with a match against Sheffield Wednesday at Hillsborough.