The conditional deal is also believed to contain proposals for a public apology from the University of Liverpool and Alder Hey officials.

The compensation is thought to amount to about £5,000 per child involved, with money left to be put in a trust fund.

Many bereaved families were forced to hold second and third funerals after they discovered that doctors had secretly stripped organs from their dead children.

Tribute to parents

A plaque at the hospital is planned to recognise that the organs were wrongly retained, and paying tribute to the parents involved.

The dispute over the retained organs went into mediation to avoid litigation.

It followed the publication of a report on the government investigation into practices at the hospital.

Since the report Alder Hey bosses have reaffirmed their commitment to changes in the law governing organ retention.

'Unforgivable' pain

The report, published in January last year and chaired by Michael Redfern QC, described as "unforgivable" the pain caused to the parents by "this dreadful sequence of events".

Other remedies are thought to include a memorial to victims and a university donation to charities nominated by the parents' trust.

News of the settlement offer also emerged on Wednesday during a brief hearing before a High Court judge in London.

Mark Mildred, a solicitor representing a group of the Alder Hey claimants, made the announcement to Mr Justice Gage during a case management conference.