Spacey was the artistic director of the Old Vic theatre, which is a registered charity, from 2004 to 2015, and is a trustee of the Kevin Spacey Foundation.
The commission has written to both charities after several men made claims of sexual misconduct against Spacey.
In a statement, the regulator said: "The commission is aware of allegations reported in the media regarding the Old Vic Theatre Trust and its response to allegations regarding the behaviour of a former senior staff member. We have contacted the charity’s trustees to seek clarification on this matter and to assess if there is a regulatory role for the commission.
"We have also contacted the trustees of the Kevin Spacey Foundation."
The statement said the regulator expected trustees to "ensure their charity has robust safeguarding polices in place", including strict procedures about how to deal with any allegations.
"Where appropriate, trustees should report them to the police as well as to the commission as a serious incident," the statement said.
Third Sector understands that the commission has received no reports or concerns about safeguarding matters at either charity, and that the commission has not opened a formal investigation.
The Old Vic published a statement on 31 October in which it said it was "deeply dismayed" about the allegations against Spacey and had set up an email address for anyone wishing to make a confidential complaint.
"Inappropriate behaviour by anyone working at the Old Vic is completely unacceptable," the statement said. "We aim to foster a safe and supportive environment without prejudice, harassment or bullying of any sort, at any level.
"We want our employees to feel confident, valued and proud to be part of the Old Vic family. Any behaviour we become aware of which contravenes these goals will not be tolerated."
Neither charity responded to Third Sector’s request for comment before publication.