The match at Loftus Road will be the first meeting of the pair since Terry was hit with a criminal charge of racially abusing Ferdinand during Chelsea's 1-0 defeat at QPR in October.
Terry, who denies any wrongdoing and has also been charged by the FA, will appear in court on February 1.
QPR intimated on Tuesday that they want Ferdinand to ease tensions ahead of the west London derby by publicly burying the hatchet with Terry.
But the Daily Mirror claim Ferdinand has been left bemused by the club's stance and maintains he has not been approached over the issue.
If Ferdinand does refuse Terry's handshake, it will not be the first time the Blues skipper has been snubbed.
Wayne Bridge refused to shake his hand ahead of Manchester City's game with Chelsea in February 2010, amid allegations Terry had an affair with the mother of Bridge's son.
Meanwhile, Bruce Buck, chairman of Chelsea, and Tony Fernandes, his QPR counterpart, have issued a joint statement to try and calm any tension among the fans ahead of Sunday's match.
"We have discussed the issues surrounding this weekend's FA Cup fourth-round tie at Loftus Road and we are both in total agreement that abuse and discrimination has no place in football or society.
"Both clubs enjoy fantastic support. However, we would remind fans that while we want to hear their passion, it's a fact that hatred and abuse is not what being a fan of Chelsea or QPR is about.
"The clubs will work together with the police to ensure that anyone using discriminatory or inflammatory language is identified and that the strongest possible action is taken against them."
The statement continued: "A local derby is always a special occasion and this weekend's FA Cup tie is a unique opportunity to show the world that hatred has no place in our game, our clubs, or our communities.
"We would urge fans witnessing any form of abuse to report it to a matchday steward or text confidentially on 07557 435421.
"Let's make Saturday's match a celebration of football."
The match has been brought forward to a midday kick-off on the advice of police in a bid to minimise potential crowd problems, with both clubs keen to avoid any ill-feeling amongst fans.