Campbell, 29, signed a four-year deal when he joined in 2001 from north London archrivals Tottenham Hotspur and had now begun negotiations over a three-year extension, the paper said.
"It is true that we are talking to Sol about a new contract," manager Arsene Wenger was quoted as saying.
"Those talks are at a very early stage but I am optimistic. He has been a fantastic signing for us and I hope he will stay even longer than his present deal."
