At this stage it is unclear whether Democratic Unionist Party leader Peter Robinson, who was admitted to hospital on Saturday after suffering an adverse reaction to prescribed medication, will be in attendance.
Mr Robinson added that he was happy to appear before the inquiry.
Mr Bryson was permitted to give his evidence in public following a committee vote by MLAs.
Political watchdogs on both sides of the border are examining the issue, while Britain’s national crime agency has launched a criminal investigation.
He said a success fee paid to Tughans went into a Danske Bank account in Belfast and was later transferred to an offshore account.
Meanwhile, tensions between Mr Robinson and Deputy First Minister Martin McGuinness emerged this morning during the inquiry into the sale of NAMA’s Northern Ireland portfolio.
Asked whether he should have been kept up to speed about meetings in which Mr Robinson was acting as first minister, Mr McGuinness said that led to his concerns.
Earlier on Wednesday the deputy first minister of Northern Ireland, Martin McGuinness, denied any wrongdoing in relation to the Nama deal, but said there were “very serious questions” for Robinson to answer.
In a hard-hitting statement, Mr Robinson said: “I repeat, I neither received, expected to receive, sought, nor was I offered a single penny as a result of the Nama sale”.
During the course of his evidence Mr Bryson made a number of allegations.
In evidence given to the finance committee at Parliament Buildings in Belfast, Mr Bryson made a series of explosive allegations and said his sources included “whistleblowers”.
He said he was conscious that he did not want to stray into any area of evidence that the committee did not want him to and said he would make “no wild allegations or innuendo”.
Some of this money, he claimed on the Dáil record, was “reportedly earmarked for a Northern Ireland politician or political party”.
In a torrent of information and allegations which MLAs found hard to comprehend, Mr Bryson also queried whether Fortress Capital, which had been bidding for the NAMA loans, had been a “stalking horse” for Cerberus.
The DUP proposal to hear Mr Bryson with the public excluded was supported by independent MLA John McCallister, but they were outvoted by Sinn Fein, the SDLP, Alliance Party and UUP.
The finance committee is examining the 2014 sale of the region’s Nama portfolio of debt-ridden properties that had to be nationalised by the republic’s government.
He also claimed that he was never consulted about an apparent memorandum of understanding between the Office of the First Minister and a rival bidder, Pimco.
Cerberus, which bought up the debt-ridden properties once owned by Irish property investors, denies that there were any improper or illegal payments made to help the sell-off.