Arsenal earn around £3million per match at the Emirates while Chelsea's income is, on average, £2.2million.
The sale of naming rights is a way of making up that shortfall although Chelsea stressed that the name Stamford Bridge would be retained in any deal and it is understood they are looking for a blue-chip partner for a long-term contract between seven and 10 years.
New Chelsea chief executive Ron Gourlay explained on Chelsea TV: "Retaining the heritage of the stadium is paramount to considering such a move, but we think that is achievable and, on that basis, we would enter into discussions over naming rights with the right partner for Chelsea.
"We understand that this is a sensitive issue for our fans and that is why we would keep the name Stamford Bridge in any deal.
"What we are not prepared to happen, and I am sure our fans will appreciate this, is to allow our rival clubs in England and Europe to gain a competitive advantage over us in terms of the revenue they can generate, through either expanding the capacity of their existing stadia or moving to a new stadium, and then invest that upside in their team or the club."