A No 10 spokeswoman said: "The stories that she heard were just that there were tensions between the chair and the panel. Nothing more than that."
In February last year the Former New Zealand High Court Judge, Dame Lowell was appointed to head the inquiry, but she stepped down in August, just days after the Home Office was made aware of concerns over her "professionalism and competence".
Dame Lowell left the inquiry in chaos when she suddenly quit her £360,000-a-year (NZ$611,000-a-year) role on August 4th. Victims and their lawyers accused her of a 'betrayal' while complaining the inquiry had 'descended into farce'.
She was the third inquiry chairman to quit following the resignations of Baroness Butler-Sloss and Fiona Woolf.
Speaking today May said she could not take action on the basis of "rumour or hearsay".
It comes after MPs accused the Home Office of a cover up and questioned how ministers could not have been aware of the 'dysfunction' at the heart of the inquiry.
Speaking during Prime Minister's Questions, May told MPs: "There were stories around about the inquiry, and about individuals related to the inquiry.
"But the Home Secretary cannot intervene on the basis of suspicion, rumour or hearsay."
They added that it was "only right to act on formal complaints and evidence."
Lisa Nandy, the Labour MP for Wigan, told the Huffington Post: "Now that Theresa May has admitted she knew of failings in the abuse inquiry whilst she was in charge of it she must explain why she took no action other than to allow a generous £80,000 (NZ$136,000) pay off to the judge at the centre of these serious allegations."
Child sex abuse inquiry
Set up: July 2014 by then Home Secretary Theresa May
Duration: Up to six years - possibly longer
Led by: Professor Alexis Jay - a former social worker who helped expose the Rotherham abuse scandal
Remit: To investigate whether institutions and organisations have taken seriously their duty of care to protect children from sexual abuse in England and Wales. These include:
• local authorities
• the police
• the Crown Prosecution Service
• the Immigration Service
• the BBC
• the armed forces
• schools
• hospitals
• children's homes
• churches, mosques and other religious organisations
• charities and voluntary organisations
Timeline
2012 - 2013 - Savile shock
Jimmy Savile is identified by police as a prolific child sexual abuser a year after his death. During the investigation into him, various media and political personalities, (as well as many others) are linked to child sexual abuse. Some are convicted and calls are made for a public inquiry.
July 2014 - Inquiry launch
Following the Savile scandal, then Home Secretary Theresa May announces an independent inquiry into the way public bodies have investigated and handled child sex abuse claims. Baroness Butler-Sloss is chosen as head.
July 2014 - First resignation
Retired judge Butler-Sloss quits less than a week after her appointment after a series of claims about her brother Michael Havers' role in previous investigations more than 30 years ago, when he was Attorney General.
October 2014 - Second resignation
City lawyer and Lord Mayor of London Fiona Woolf, the second new head of the inquiry, steps down just weeks after her appointment. It emerges she had five dinners with former Home Secretary Lord Brittan from 2008-2012.
February 2015 - Third time lucky?
Senior New Zealand judge Justice Lowell Goddard becomes the new head of the inquiry. The inquiry is also given new powers as a statutory inquiry and the original panel is disbanded.
November 2015 - Unprecedented scope
Justice Goddard announces that 12 separate investigations are to take place as part of the unprecedented inquiry, including investigations into MPs, local councils, and church organisations. In January 2016, a 13th investigation is launched into Lord Greville Janner.
August 2016 - Third resignation
Dame Lowell Goddard becomes the third chairman to resign following criticism over the scale of her pay and benefits and also the amount of time she has spent abroad since taking on the role.
August 2016 - Fourth appointment
Professor Alexis Jay, a former senior social worker who previously led an inquiry that revealed at least 1,400 children were subjected to sexual exploitation in Rotherham, is named as the fourth chair.
September 2016 - Top lawyer leaves job
Ben Emmerson QC is suspended, then resigns, after claims of a clash over the scope of the inquiry.
October 2016 - Change of scope
Professor Jay says it is unrealistic to hold a public inquiry style hearing into every one of the thousands of institutions where abuse is said to have occurred.
Instead, the inquiry is to focus on four main "thematic strands" in order to ensure that lessons were learned from the failings of the past.
In this way, she believes: "We can complete a significant amount of the inquiry's work by the end of 2020."
