The person spoke on condition of anonymity because McCarthy's deal was pending a physical.
The physical will be especially important for McCarthy, who was Oakland's opening day starter last season.
McCarthy was hit in the right side of the head by a line drive off the bat of the Los Angeles Angels' Erick Aybar on Sept. 5. The 29-year-old pitcher sustained an epidural hemorrhage, brain contusion and skull fracture, then underwent a two-hour surgery.
Last month, McCarthy spent two days undergoing extensive evaluations by renowned concussion expert, Dr. Michael Collins, at the University of Pittsburgh. He was cleared by Collins to begin working out and resuming his regular offseason routine.
Oakland's medical staff initially warned that McCarthy's situation was very much "life-threatening.''
Now, McCarthy checks in with Dr. Collins once a week to let him know that everything is going well, or if something seems a little off. McCarthy said in November that his concussion symptoms had subsided, but he still has to use caution and take notice of everything when exerting himself.
McCarthy went 8-6 with a 3.24 ERA this year in his sixth big league season and second with the A's. He was 9-9 with a 3.32 ERA in 2011.
McCarthy, who didn't immediately respond to messages Friday, said he planned to begin playing catch this month, then throw bullpens starting in January if all continues to go well.