Edwards iscurrently in hospital receiving treatment for mental health issues, his wife said.
The exchanges allegedly began in 2020 when the young person was aged 17.
His wife Vicky Flind, herself a prominent TV producer, said he will respond when able.
BBC Director General Tim DavieGetty
Davie said: This remains a very complex set of circumstances.
Also this evening,The Sunissued a statement saying that it would not be publishing further allegations against Edwards.
It stood by its reporting and said it would cooperate with the BBCs probe.
Many of you will have read the words of Vicky Flind, Huws wife.
It is a reminder that the last few days have seen personal lives played out in public.
At the heart of this are people and their families.
This will no doubt be a difficult time for many after a challenging few days.
I want to reassure you that our immediate concern is our duty of care to all involved.
As you know, we were asked to pause our fact finding investigations until that assessment had been concluded.
It is important we now continue with this work.
I want to be clear that in doing so we will follow due process.
This remains a very complex set of circumstances.
Further serious allegations have emerged in the past few days.
The Sunwill cooperate with the BBCs internal investigation process.
The Sunhas no plans to publish further allegations.
Suggestions about possible criminality were first made at a later date by other media outlets, including the BBC.
We reported that the parents had already been to the police who said that they couldnt help.
The parents then made a complaint to the BBC which was not acted upon.
It is now for the BBC to properly investigate.
