Alonso, who injured the knee in Week 2 against the Dallas Cowboys, could return to the Eagles as early as a few weeks from now, the source said.
It was originally thought that Alonso had suffered a significant ACL tear, but further testing showed that was not the case.
The main reason he is expected to play again this season is that there is good stability in his left ACL, the source said.
Eagles coach Chip Kelly said Wednesday that Alonso was rehabbing the knee and that the team would see him Friday. Kelly has been asked a few times about the injury since Week 2, but only would say that Alonso had a sprain.