Greek giants Olympiakos have been linked with a loan move for the Cameroon international before the close of the window.
Makoun, who joined Villa last January from Lyon, after being brought in by Gerard Houllier does not appear to figure in McLeish's long-term plans.
The 28-year-old has been an unused substitute in Villa's opening two Premier League games and has made just seven appearances since arriving at Villa Park.
Asked about Makoun possibly leaving Villa, McLeish admitted: "It's possible but we wouldn't let anybody go unless somebody came in."
Source: Team Talk
Source: Team Talk