The complaints stemmed from Chelsea's 3-2 defeat at the hands of Manchester United on October 28, a match in which Clattenburg sent off Branislav Ivanovic and Fernando Torres of Chelsea.
Clattenburg has denied making inappropriate remarks.
The Metropolitan Police closed their investigation into the matter on Tuesday, while the Football Association says it will complete its own probe by Friday.
By then it will be almost three weeks since the match and Cech is eager to move on.
"For me it is difficult to comment on something that I didn't hear or was not even involved or even close to," Cech said.
"I believe that if you come with something like that, you need to have a really good case to say it because if not it would waste the time of everybody and again it wouldn't be good for football.
"If there was a case it is not because Chelsea want to do something, it is just because there is a case and, again, I hope that this story will be finished as soon as possible."
Whatever the outcome of this particular case, Cech wants to see better communication between players, referees and fans in the future to reduce the number of disputes.
"I think there should be better communication from the side of the referee towards the public as well," he added. "I think it would help."
Cork sign Kavanagh
CORK CITY have completed their first major signing of the close season with the capture of striker Daryl Kavanagh from Shamrock Rovers, writes Aidan Fitzmaurice.
The Waterford-born player caught the eye for St Patrick's Athletic in 2011 but struggled at Rovers last season. But Cork boss Tommy Dunne remains a fan and hopes he can help City make a challenge next season.
Meanwhile, Sligo Rovers defender Alan Keane has put pen to paper on a new deal.