The 29-year-old has been absent since suffering knee ligament damage in the first leg of the quarter-final win against CSKA Moscow on April 5.
Wenger had hoped to get Mkhitaryan back involved within a month, and the latest prognosis suggests that the Armenian playmaker has a chance of being fit for next Thursday's meeting with Atletico.
"Mkhitaryan is running again," he told reporters ahead of the visit of West Ham United this weekend. "He has to progress in the next three of four days to see how much intensity he can have in his training sessions. Next Thursday is the earliest date for his return."
Five goals and a further two assists have been provided by Mkhitaryan since swapping clubs with Alexis Sanchez in January.