The interviewees are understood to have included Clattenburg plus assistant referees Michael McDonough and Simon Long and fourth official Michael Jones.
The interview process was expected to be completed on Thursday night or Friday, enabling a decision on whether any action should be taken by the FA to be made early next week.
Chelsea submitted a dossier of evidence to the FA containing signed witness statements from players, who allege Clattenburg used a term understood to have been interpreted as racist during the Premier League match against Manchester United on October 28.
The full file of evidence from Chelsea was received by the FA at the start of the week and since then the players have also been interviewed.
The case could not be more sensitive following Chelsea skipper John Terry's four-match ban for racist abuse, and the FA is determined to deal with it as quickly as possible - especially following criticism about the time, almost a year, it took to deal with Terry.
Clattenburg, meanwhile, has decided not to referee a match for a second consecutive weekend while the investigation is ongoing.
The Metropolitan Police has also launched an investigation following a complaint lodged by the Society for Black Lawyers, based on reports of the incident rather than any evidence.
Manchester United manager Sir Alex Ferguson has had his say, saying it was "unthinkable" that Clattenburg would make such a comment and that he was "convinced" he would not have done so.
Clattenburg, 37, who is on FIFA's shortlist to be a match official at the 2014 World Cup, strenuously denies the accusations against him.
Source: PA
Source: PA