Unai Emery sees the forward as a priority for this window, although it has so far been a protracted process between the clubs.
Middlesbrough are understood to want around £10m for the 21-year-old, although a figure has not actually been given to Villa as the preference is to keep a highly-rated player only signed in the summer.
Rogers came from Manchester City where he was considered an excellent youth prospect.
The player is said to consider a prospective move to Villa as a huge opportunity. The Birmingham club’s opening bid was understood to be around half what would make Middlesbrough consider a sale.