On 30 June, the trust reported a year to-date deficit of Â£738,000 compared to a planned shortfall of Â£125,000.
Monitor said the trust's "finances will continue to deteriorate" and is yet to decide on whether further regulatory action is needed.
The BCPFT said its finances were its "biggest challenge".
Karen Dowman, chief executive of the trust, said: "We have already started a programme of activity to identify cost-savings and improve our financial sustainability, and to put in place safeguarding checks to ensure efficiencies do not compromise care."
Marianne Loynes, regional director at Monitor, said: "No decision has been taken about whether further regulatory action is required and an announcement about the outcome of the investigation will be made in due course."
The trust provides mental health, learning disability and community healthcare services across Sandwell, Dudley, Walsall and Wolverhampton.
The Black Country Partnership NHS Foundation Trust (BCPFT) is being investigated by a health regulator due to concerns over its finances.