The centre half got the injury in the latter stages of a 0-0 draw with Manchester United before the international break.
However, manager Unai Emery did not know if his defender would be out for a long time.
Emery said: "I don’t know if it’s a big or small injury”.
Now The Telegraph states that Konsa is of the belief that he will be back in time for the Premier League’s return in less than a fortnight.
Villa will take on Fulham at Craven Cottage after the break, followed by a Champions League game against Bologna at home.