According to Sky News, Mr Swannell, who was previously the former chairman of CitiGroupâs European investment bank, will succeed Sir Stuart Rose in the post when the latter steps down next year.
The former banker, who is currently chairman of HMV, has worked with the retailer in the past as an advisor.
He helped the firm avoid a takeover attempt from entrepreneur Philip Green back in 2004 in his advisory role while he currently holds positions as a non-executive director at British Land and 3i Capital.
Nick Bubb, analyst at Arden Partners, told Reuters: âHe's a well-respected City heavyweight, kind of what they need. Because it's M&S there's always a lot of focus on who the chairman is."
âIf it is Robert Swannell it will be a bit more low key (than Rose)," he added.
News reports suggested that if Mr Swannell is appointed to the role, then it should help M&S improve its relationship with the City.
By Jim Ottewill