The Daily Mail says Campbell will complete a shock £20,000-a-week return to Arsenal in the next few days.
The 35-year-old defender has been training with Arsene Wenger's side since walking out on Notts County in September after one game. He will sign for them on a free transfer until the end of the season.
Campbell played the first half of the Gunners' reserves game against West Ham at Upton Park on Tuesday night and has been pencilled in for the FA Cup fourth-round tie against Stoke City on January 24.
After his side's 4-2 win Campbell said. "I felt fine - 45 minutes was enough after four months out."