The Daily Mail says the United veteran will discuss the issue with manager Sir Alex Ferguson before deciding if he will ignore his former England team-mate during the pre-match ritual.
Ferdinand wants to respect Ferguson's views, particularly after last weekend's controversy where the United boss criticised the 33-year-old for not wearing a Kick It Out anti-racism T-shirt.
Ferdinand also wants to show solidarity with his brother Anton after Cole gave court testimony in favour of John Terry earlier this year as the Chelsea skipper was found not guilty of racially abusing the Queens Park Rangers defender in October 2011.
It is understood Cole is willing to shake Ferdinand's hand before the game at Stamford Bridge. The United man was fined £45,000 by the FA for appearing to endorse a tweet describing Cole as a 'choc ice' - a slang term with clear racial connotations.