"Talks are ongoing with Sol with a view to a permanent move back to Arsenal Football Club," the Premier League club said on their website.
Campbell, 35, who left Arsenal in 2006, has been training with his old club since ending a brief spell at League Two Notts County this season. Before that he spent three years at Portsmouth.
Arsenal manager Arsene Wenger, who has never re-signed a player during his 13 years in charge, has praised free-agent Campbell over the last few weeks and has not ruled out a move for him.
Campbell, former captain of arch-rivals Tottenham Hotspur, moved across north London in 2001 and in his five years at Arsenal the club won two Premier League titles and three FA Cups.
He was also part of the team that won the FA Cup and league double in 2002 and the side that was undefeated during the 2003-04 league season.
Campbell's last match for Arsenal was the 2006 Champions League final when he scored in their 2-1 defeat by Barcelona.
He won the last of his 73 caps in November 2007 when England lost to Croatia at Wembley and were eliminated from Euro 2008.
While Campbell moved closer to a return, the club's Swiss international defender Philippe Senderos said he wanted out.
"I want to go, I want and need to be playing ahead of the World Cup," he told the BBC. "I don't want to play in the reserves, I just want to go."
