Barrister Mark McDonald added: “The police have been briefing about further enquiries for over a year.
“Any allegations need to be taken seriously so we are only surprised by the timing of this new leak from the police.”
The police statement confirming Letby had been quizzed over more baby deaths followed reporting in the Daily Mail, external.
The force said more information would be released “at the appropriate time”.
Letby is serving 15 whole-life orders for murdering seven babies and attempting to murder seven other infants between June 2015 and June 2016.
Letby, originally from Hereford, made two attempts to kill one of her victims.
Following her convictions, Cheshire Constabulary revealed officers were investigating the time she had spent on two placements at Liverpool Women’s Hospital.
It is part of a wider examination into Letby’s whole career.
This involves reviewing more than 4,000 admissions into neonatal units where Letby had been present.