Carter retroactively tested positive for the banned stimulant methylhexaneamine at Beijing and was stripped of the gold along with Bolt, Asafa Powell, Michael Frater and Dwight Thomas.
Carter appeared at the Switzerland-based Court of Arbitration for Sport in November to appeal against the sanction and the tribunal's Secretary General Matthieu Reeb said a decision was imminent.
"I am confident that the Carter case can be finalised on or before Thursday this week," Reeb told the Inside the Games website.
The Jamaican team were ordered by the International Olympic Committee to return their medals in Jan. 2017.
Carter, the first-leg relay specialist, has been a vital member of Jamaica's dominant squad, helping the Caribbeans win golds at the 2012 London Olympics and three successive world championships from 2011-15.
(Reporting by Kayon Raynor; Editing by Ian Ransom)
