It will be the first time Mr Mackay has set foot in the Scottish Parliament since he resigned as finance secretary in 2020 over messages sent to a 16-year-old boy.
He has already submitted written evidence to the public audit committee as part of its ongoing probe into the delayed Ferguson Marine ferries.
Two vessels, the Glen Sannox and the as-yet-unnamed hull 802, are at least £150 million over budget and five years late.
A report by Audit Scotland previously found there was “insufficient documentary evidence” to explain why the contract was given to the Ferguson shipyard in Port Glasgow, which has since been nationalised, without a full refund guarantee.
Mr Mackay, who was transport minister at the time, was asked what assessment he had undertaken before recommending approval of the contract in 2015, “despite significant risks and concerns raised by CMAL”, the Scottish Government’s ferries procurement agency.
In a written response submitted in June, he said there was “a high level of confidence in the yard, which had successfully completed other vessels for the CalMac fleet”.
Mr Mackay will give evidence to the public audit committee in person on Thursday morning.
David Middleton, the former chief executive for Transport Scotland, is also scheduled to appear.
Mr Mackay disappeared from the public eye after his resignation, but clung on as an MSP until the end of the parliamentary term in 2021.
This led to calls to change Holyrood’s rules to allow the public to remove sitting MSPs under certain circumstances.