Mr Mackay was transport minister when the contract was approved to build two ferries at the Port Glasgow shipyard.
He resigned from the Cabinet in 2020 after it emerged he had sent hundreds of messages to a 16-year-old schoolboy, and he stepped down as an MSP at the end of the parliamentary term in 2021.
The public audit committee has now invited him and former Transport Scotland chief executive David Middleton to give evidence after Holyrood’s summer recess.
The former SNP minister has already provided written evidence to the committee, in which he said there was a “high level of confidence” in the shipyard.
Following the award of the contract in 2015, the construction of the two CalMac ferries was plagued with delays and the shipyard was nationalised.
The two vessels – the Glen Sannox and the as-yet-unnamed hull 802 – were originally due to be completed in 2018, but have since been delayed until at least 2023 and costs have more than doubled from the original price tag of £97 million.
Committee convener Richard Leonard said: “Yesterday we agreed to invite Derek Mackay, former minister for transport and islands, and David Middleton, former chief executive of Transport Scotland, to give oral evidence.
“This will allow us to follow up on issues in their written evidence to further inform our scrutiny of the auditor general’s report ‘New vessels for the Clyde and Hebrides’.
“We look forward to hearing from them after the parliamentary summer recess.”
If Mr Mackay gives evidence in person, it will be his first return to the Scottish Parliament since he quit the Cabinet.
On Thursday, the public audit committee was told that officials from the Scottish Government’s ferry-owning company CMAL did not want to announce publicly Ferguson Marine as the preferred bidder in 2015.
The CMAL officials said the cost overrun was down to “catastrophic contractor failure”.
Separately, another Holyrood committee announced on Friday that it would hold its own inquiry into the future of ferry provision in Scotland.
The net zero, energy and transport committee has called for views on what a “modern and sustainable ferry service” should look like.