Malcolm Webster, 52, was found guilty two weeks ago by a jury in Glasgow of murdering his first wife and attempting to murder his second wife to get their life insurance payouts.
The Scotland on Sunday newspaper says police are investigating claims linking Webster to suspicious deaths in a Middle East hospital where he worked as a nurse for six months.
It is claimed Webster was fired from the Abu Dhabi hospital after special needs child patients - all under six years old - suffered fatal cardiac arrests while he was on duty.
He was suspended after the third death but no charges were brought.
Webster's first wife, Claire Morris, died in what seemed to be a fiery car crash in Scotland in 1994.
Five years later in Auckland, Felicity Drumm narrowly escaped death in similar circumstances several times and discovered that Webster had cheated her of her life savings.