The deputy prime minster has admitted he was aware of allegations against Lord Rennard in 2008. Lord Rennard, the party's former chief executive, has strenuously denied the allegations.
But there is growing criticism that the party failed to properly investigate the complaints when they were first made, and senior party figures said over the weekend that Clegg had been unaware of them.
Speaking on BBC Radio Solent on Monday morning, the Lib Dem leader said the priority was to "listen to the women."
He added: "I have got absolutely nothing to hide. Why would I? I know some of these women very well - one of them worked for me. I spoke to her last night...she never said any of this to me."
Clegg repeated that "no specific allegations" had been made before a broadcast by Channel 4 News, which interviewed some of the women involved. Previously those involved had not wanted to reveal their names, he said.
He added: "Now they have developed into specific allegations, we can act and we will."
Party president Tim Farron acknowledged that the party had "screwed this up" and failed in its duty of care.
He said a "completely full and open inquiry into how we got this wrong" was under way and insisted that he had heard only a "general rumour" before the complaints were broadcast.
"The one thing I probably can tell you without going through due process is that we screwed this up as a party," he told the BBC Radio 4 Today programme.
Asked when he first heard of allegations against Lord Rennard, he said: "A general rumour I heard a year or so ago but no specifics, not even who or what or when or anything."
Clegg's former chief of staff Danny Alexander - now Chief Secretary to the Treasury - confronted Lord Rennard with the claims and "warned him that any such behaviour was wholly unacceptable" after general concerns were raised in 2008.
Questions have also been raised as to what, if anything, former Lib Dem leaders and other senior figures had heard about the allegations.
Sir Menzies Campbell, who led the party between 2006-2007, is currently in Brussels and not available for comment.
Simon Hughes, party president between 2004 and 2008, insisted that no specific or general concerns were raised with him at the time.
On Sunday business secretary Vince Cable said he was not aware that there was any reason for Lord Rennard stepping down in 2009 other than health issues.
David Cameron's official spokesman said today that the Prime Minister regarded all forms of harassment as "unacceptable". But the spokesman declined to comment directly on the allegations against Lord Rennard.
Asked about the Rennard affair at a daily Westminster press briefing, the PM's spokesman said: "I am not going to get into the allegations that have been reported in the press in recent days.
"I would simply make a general point that of course harassment of all kinds is unacceptable. With regard to the current series of allegations, that is a matter for the Liberal Democrat party."
Asked if Cameron had full confidence in Clegg and in Jo Swinson, the spokesman replied: "He does."Suggest a correction