The other member of the commission is former Supreme Court judge Justice (retd) Madan B Lokur.
"Deposition of those claiming to have got directly affected will commence from December 13," Bhattacharya said.
The former chief justice of Calcutta High Court also said that political strategist Prashant Kishor was supposed to depose before the panel on Wednesday, but did not.
"We had sent notice to Prashant Kishor, a date was fixed for his deposition yesterday, but he did not come or join," he said.
There is a provision for appearing before the commission both physically or over the virtual mode.
"We have not yet rescheduled Kishor' desposition," Bhattacharya told PTI, adding that a new date will be fixed after getting confirmation from him.
According to reports, his name was among those whose phone numbers were listed as potential targets in the alleged snoopgate. Bhattacharya maintained that two experts on cyber crime are scheduled to make submissions before the commission this week.
Deposition of informants , which commenced from November 29, has concluded, Bhattacharya said.
He also said that two lawyers from Delhi have deposed before the commission, giving information on the whole controversy.
"One of them was Apar Gupta who helped with information in matters relating to the snooping row before the Supreme Court and also on cyber issues," he stated.
He said that two more persons, one from Pune and another from Uttar Pradesh, deposed before the commission on Thursday.
"None of them are directly affected. Such people (ones directly affected) will appear before the commission in the next phase," Bhattacharya underlined.
He further explained that people claiming to be directly affected by the alleged phone tapping using Israeli spying software have submitted their affidavits to that effect before the commission.
Among these people are one joint founder editor of a well-known news portal and a veteran journalist, the former chief justice added.
With PTI inputs.