A senior Tory source confirmed that party officials were taking written statements from around 40 "witnesses" including the Lord.
The row over alleged behaviour by Mark Clarke shows little signs of abating despite the resignation of international development minister Grant Shapps, who said he believed the "buck should stop with me".
The departures of Mr Shapps and Lord Feldman had been demanded by the father of a Conservative Party activist who killed himself, leaving a note condemning Mr Clarke – who denies any wrongdoing.
The final straw for Mr Shapps appears to have been the emergence of an email sent to him by ex-minister Baroness Warsi in January, complaining that the election campaign aide had been abusing her on Twitter.
The party had previously insisted no complaints against Mr Clarke, who ran its RoadTrip canvassing drive in the run-up to the election, were received before August. He has since been expelled.
In a letter to David Cameron confirming his departure, Mr Shapps - who was co-chairman with Lord Feldman until the election - wrote: "Although neither the party nor I can find any record of written allegations of bullying, sexual abuse or blackmail made to the chairman's office prior to the election, I cannot help but feel that the steady stream of those who raised smaller, more nuanced, objections should have perhaps set alarm bells ringing sooner."
Downing Street has stressed that Lord Feldman retains the "full confidence" of Prime Minister David Cameron.
Lord Feldman is understood to have launched the investigation into the allegations surrounding Mr Clarke in August, but has never played a part in it.
Clifford Chance LLP has been instructed to prepare a report on the issues raised, with a remit to assess whether complaints were handled properly and "identify any individuals who were at fault".
The firm's lawyers will also consider the integrity of the evidence-collecting process and whether the right people have been interviewed.
The collection of evidence is not expected to be completed until the end of the year, and Clifford Chance will produce the report "as soon as possible after that".
The source added: "It will be a decision of the board which parts of the report to publish having regard to protecting vulnerable witnesses, the ongoing coroner's inquiry and police investigation. Subject to this, the party intends to publish the key findings and recommendations."
Defence Secretary Michael Fallon said Mr Shapps had taken responsibility for the scandal but stressed the party needs to see "where the investigation takes us".
He told BBC One's Andrew Marr Show: "The person directly responsible for central office, for campaigning, the co-chairman Grant Shapps, who signed up Mark Clarke's operation - he has accepted responsibility and yesterday he resigned.
Asked whether Lord Feldman should resign, he said: "It was Grant Shapps who was in charge of campaigning and who was involved in this and I think it's best now to see where the investigation takes us."Suggest a correction