Coram established the museum in 1998 to care for its Foundling Hospital Collection, which includes sculptures, manuscripts and paintings by William Hogarth, including his portrait of Captain Thomas Coram, founder of the children’s charity.
A legal ruling by the Attorney General when the museum was set up in 1998 gave it 25 years to raise funds equivalent to the market value of the collection.
Coram set up the Foundling Museum as a separate charity because its articles did not give it the power to administer an art collection. The museum’s annual report for 2011/12 said that Coram had the power to appoint four of the museum’s 10 trustees.
In June this year it was reported by the Guardian newspaper that in 2012 Coram changed the museum’s articles to allow it to remove trustees.
On 23 May this year, Coram informed six trustees by letter that they had been sacked, including Jeremy Deller, a Turner Prize-winning artist.
Concerns were raised with the Attorney General’s Office, which wrote to Coram earlier this year about the removal of the trustees. A spokesman for the Attorney General’s Office said it had now passed the matter to the commission.
A spokeswoman for the commission said: "The commission is aware of current difficulties that exist between the Thomas Coram Foundation and the Foundling Museum and we are keen to see these resolved in the best interests of both charities.
"We have met with the representatives of the foundation and with the dismissed trustees to enable us to understand these difficulties better and have been assessing a number of key issues that deal with the relationship between the foundation and the museum.
"We are treating this as a matter of priority and will shortly be writing to those involved setting out our provisional views on these issues in the hope that this clarity will enable a satisfactory way forward to be found."
The commission spokeswoman said the regulator met with representatives from Coram at the end of June this year and with the former museum trustees in mid-July.
A spokeswoman for Coram said in a statement: "Some former trustees of the museum felt things should be done differently and their opinions were, in view of professional advice to the Coram board, considered incompatible with the charity’s charter. The commission is aware of this background.
She added: "The Coram collection of historic works of art will be maintained and protected and is on display at the Museum to be enjoyed by all."