It came as the First Minister said she is serious about holding a second independence referendum next year and internal critics are "wrong" to say this is unlikely to happen.
She said nothing had changed in terms of her timetable and she is delivering on a mandate she won in the Holyrood election last year.
Ms Sturgeon spoke to Scotland on Sunday onboard the SNP’s campaign bus, which will tour Scotland ahead of the local elections on May 5.
She said the election is an opportunity to put the cost of living crisis centre stage and “send a message” to Boris Johnson over partygate.
And she denied accusations her government had underfunded councils in Scotland.
Mr Mackay is said to be willing to “answer any questions” from MSPs over the deal to build two new ferries for CalMac, which are now years overdue and hugely over budget.
He reportedly feels “victimised” after Ms Sturgeon appeared to blame him for giving the green light to the contract, and wants to “set the record straight”.
The former finance secretary has not been seen in Holyrood since February 2020, when he dramatically quit over messages sent to a 16-year-old boy.
The Glen Sannox and another vessel, known as hull 802, are still under construction at the now government-owned Ferguson shipyard in Port Glasgow, although neither will be in service until at least next year – five years later than planned.
The bill for the two ferries has risen to at least £240 million, two-and-a-half times their original price tag.
Holyrood’s public audit committee is now poised to launch an inquiry into the debacle.
Asked if she was worried about Mr Mackay giving evidence and the information he could put into the public domain, Ms Sturgeon, who said she had not spoken to the former minister since around the time of his resignation, insisted: "Not in the slightest."
Asked if the public knows “everything there is to know”, the First Minister said: "I believe so, yes.
"And actually, most of the information that has been all over the media in recent weeks has actually been in the public domain for two or more years, it's just that nobody has chosen to make it what it's been, and that's up to the media and opposition politicians.
"But there's nothing that's been in the media, in terms of the issues that have been canvassed over the past few weeks, that hasn't been in the public domain, published by the Scottish Government for a long, long time."
Ms Sturgeon has expressed her “regret” over the ferries situation, but is visibly frustrated when asked why she won't apologise to islanders.
"Oh for goodness' sake,” she said. "Well look, you can decide to make comments about the words.
"I choose my own words. It's one of the few things I still can decide for myself.
"I choose my own words. I deeply regret it for island communities, and also in a broader sense, and I'm very focused on making sure we are supporting the shipyard and the new management of the shipyard to get the ferries completed and then secure a future for that shipyard.
"Because what I don't regret is saving the shipyard, because I think it's really important that Ferguson shipyard continues, with the 400 or so more jobs now than was the case when it first was saved, and that we continue to support those jobs into the future."
The First Minister wants to hold a second independence referendum before the end of next year, but the UK Government is unlikely to agree to this.
Kevin Pringle, a former senior member of staff within the SNP, recently said another vote is “unlikely to take place” in this timescale “given the hurdles to be overcome and extensive preparations required”. SNP MP Joanna Cherry has said the debate is “stalled”.
Ms Sturgeon insisted she is serious about holding a referendum next year and said others are “entitled to their opinions”.
She said: “Kevin's a commentator, somebody I respect highly but I think he's wrong on that.
"I've set out the timetable I'm working to. Nothing has changed around that.
"Plans for that are underway, so nothing has changed. I won the mandate for that in an election this time last year."
A recent poll published in The Scotsman showed a majority of Scots think discussions over when a second referendum should take place should stop due to the Russian invasion of Ukraine.
Ms Sturgeon said: "Look, in politics, of course you look at opinion polls, but I won an election on this timetable and plan, so that's the plan I'm working to.
"I accept, I've always accepted that to win a referendum, which is actually the important thing, I've got to persuade a majority of people that independence is the right thing for Scotland. That's what I am planning to do."
She said Indyref2 legislation will be published "in due course", adding: "I haven't decided on the specific date for that right now.
"Plans are underway but I will confirm that when we have got to that point."
Elsewhere, the First Minister said there needed to be “really robust” climate assessments before any new oil and gas fields get the go-ahead in the North Sea.
The UK Government’s recent energy strategy said a licensing round for new projects is planned for the autumn.
"Any decisions on new licenses have to be decided against a really strict assessment of compatibility with our net zero ambitions,” she said.
Ms Sturgeon said she did not accept that the Scottish Government had underfunded councils, insisting it has “prioritised local services to the best of our ability”.