Manager Alex Cora said that Abreu (calf) progressed to running the bases Sunday, Tim Healey of The Boston Globe reports.
The 26-year-old is trending toward returning from the injured list this week, and getting back to running the bases is a significant hurdle to clear. Abreu has been on the shelf nearly a month due to a calf strain, but he may not require a rehab assignment before rejoining the Red Sox.