Mr Ryall, who in a statement earlier this month said he was "anxious for public confidence to be restored in the Otago DHB", did not respond to questions on the rumours.
In the statement, he had said the people of Otago were still asking who would take responsibility for the $16.9 million fraud which resulted in the convictions of Michael Swann and Kerry Harford.
Mr Ryall and Mr Thomson will discuss the background to the fraud.
Mr Thomson said yesterday the rumours about a possible replacement had not reached him, so he was not in a position to comment.
As far as he was concerned it was "perfectly appropriate" that he brief Mr Ryall about the fraud, as he had done with previous health ministers.
He had contacted Mr Ryall's office before Christmas offering this, but the minister's office did not contact him until this month, when it requested the "please explain" meeting.
"I want to ensure his views are fully informed by all the background," Mr Thomson said.
It is understood the Government may already be canvassing possible contenders for Mr Thomson's job for their suitability and interest in the position, but nobody is willing to say anything officially.
Requests for an interview with Mr Ryall yesterday were unsuccessful, with his office saying he was unlikely to comment about the meeting beyond his earlier statement.
Mr Thomson may be the only district health board chairman in the country who is also an elected member, so if he was removed as chairman he would still have a seat on the board.
At the last election, in 2007, when news of the then alleged fraud had already broken, he was the second highest polling candidate behind Judith Medlicott.
On the question of the fraud, Mr Thomson has said he acted when concerns were raised with him and it was difficult to know what else he could have done.
Mr Thomson, who served on the Otago Area Health Board before the introduction of district health boards, was appointed chairman of the first board in 2001 by then Labour Party health minister Annette King.
He had stood for election that year, but failed to gain a seat, although he stood successfully in the following two local government elections.
The board's former chief information officer, Michael Swann, and his friend and business associate, Kerry Harford, are awaiting sentencing on charges relating to defrauding the board of $16.9 million between 2000 and 2006 by charging for computer-related services never provided.
