Professor Steve Field and David Loughton, who run Wolverhampton and Walsall NHS trusts, are the subject of the NHS England review.
Professor Field is chairman of both trusts, while Mr Loughton is chief executive of the Royal Wolverhampton NHS Trust and interim chief executive of Walsall Healthcare Trust.
The Health Service Journal, a news organisation which covers the NHS, says the allegations came from whistle-blowers in Walsall.
A spokeswoman for Walsall Healthcare Trust said: "Our organisation is fully cooperating with the review.
"We believe it is important that everyone involved has the opportunity to speak freely and feels supported to raise any concerns they may have."
A spokesman for NHS England’s regional team in the Midlands added: "It is vital that all NHS staff feel comfortable raising concerns about the organisations they work for. An independent review into these claims is currently underway."
Mr Loughton became the interim chief executive of Walsall Healthcare Trust in April.
It followed the trust being rated "inadequate" for its medical care by the health watchdog, called the Care Quality Commission.
In taking up the position, Mr Loughton has a shared role in both trusts.
He is the longest serving chief executive in the NHS and has held his role at the Royal Wolverhampton NHS Trust for more than 17 years.
Speaking after his appointment in April, Mr Loughton said: "I look forward to working with the team at Walsall on the next steps of this journey, with a continued focus on the health and wellbeing of staff and improving the quality of care, and outcomes for the people of Walsall.
"Another area we will be focussing on is increasing our substantive workforce, in particular within nursing, to reduce the reliance on agency staffing and improve our quality of care to patients.
Professor Steve Field CBE, added at the time: "Undoubtedly, Walsall Healthcare NHS Trust has been on a journey as they focus on improving care, areas of development and building on their good practice such as innovation and compassionate patient care."