The Scottish Secretary is one of four MPs expected to be on Mr Johnson’s resignation honours list, along with former culture secretary Nadine Dorries. It is understood COP26 President Alok Sharma and former minister Nigel Adams are the other MPs that have made the cut.
They are reported to have agreed to put off heading to the Lords until the end of the current Parliament so they do not trigger by-elections.
However, on Tuesday morning a spokesman for Mr Jack insisted he was “committed” to his constituents, but did not say if the Dumfries and Galloway MP would stand again.
They said: “We cannot comment on speculation about peerages. Alister Jack is absolutely committed to representing his constituents and working with the Prime Minister to continue to deliver for people in Scotland.”
With Tory polling having plummeted, Mr Jack remaining in the Commons would save Tories the battle of retaining his Dumfries and Galloway, which he won at the last general election with less than 2,000 votes over the SNP.
Mr Sharma retained his Reading West seat in 2019 by a little over 4,000 votes from Labour, and with the Tories’ polling having plummeted they would be fearful of losing it.
The SNP are demanding a by-election in Mr Jack’s constituency and accused the Tories of “running scared of democracy”.
SNP deputy Westminster leader Kirsten Oswald said: "If Alister Jack wants to pop off to the archaic House of Lords, he should stand down now and call a by-election, so voters in Dumfries and Galloway can have a say.
"Voters deserve better than a Baron-in-waiting biding his time until he can cash in on a £300-a-day job for life in the Lords. Unlike Mr Jack, who has rubber-stamped Brexit, Tory austerity cuts and every damaging Westminster decision imposed on Scotland, an SNP MP would work hard every day to stand up for people in Dumfries and Galloway.
"This whole shoddy saga shows, yet again, that the Westminster system is beset by cronyism and rotten to the core.”
Shadow Secretary of State for Scotland, Ian Murray, claimed Tories were looking for a way out.
He said: “With Labour ready to replace this rotten Tory Government, it’s little wonder that ministers are desperately looking for an escape route. But if Tory politicians had any confidence in their shameful record they would stand in front of the people and defend it in a general election now.”
The Lib Dems urged Mr Jack to turn down the peerage, and claimed Mr Johnson “doesn’t deserve” a resignation honours list.
Liberal Democrat chief whip Wendy Chamberlain said: “He was forced from office by his own lies, corruption and law-breaking, so he shouldn’t be allowed to hand out honours to his friends on the way out.
"Alister Jack offered excuse after excuse for Boris Johnson’s appalling behaviour. He shouldn’t be allowed to slope off to the House of Lords to pass judgment on our laws for life. I hope he will recognise the already bloated size of our upper house and refuse to accept a peerage.
"The Liberal Democrats have long fought to try and get an accountable House of Lords – we must have a properly elected second chamber. Even without such fundamental reform, the House should be reduced to a sensible size. These appointments show that we are still as far away from that as ever."
According to reports, Mr Johnson’s former chief of staff Dan Rosenfield and deputy Ben Gascoigne will also get peerages.
Mr Johnson has also nominated two advisers to become the youngest life peers in history.
The advisers are Ross Kempsell, 30, and Charlotte Owen, a former assistant to Johnson, who is believed to be in her late 20s.
Mr Jack was appointed as Secretary of State for Scotland by Mr Johnson in 2019, and was reappointed by both former prime minister Liz Truss and Mr Sunak.
Others nominated for peerages include Ben Houchen, the Tory mayor for Tees Valley, and Kulveer Ranger, a former adviser to Mr Johnson at City Hall.
It came as a Cabinet minister said he believes the House of Lords was due for reform, “not least” owing to its size.
But work and pensions secretary Mel Stride said it would be “very difficult” to get political consensus on any possible shake-up, despite his belief there were “few” in the House of Commons who would oppose a change.
Deputy Labour leader Angela Rayner demanded the Prime Minister rejects the “disreputable” and apparently unprecedented demands of his Downing Street predecessor.
Ms Rayner said: “This disgraced ex-prime minister’s plot to dodge democracy by trying to reward his MP lackeys with promised jobs for life in the House of Lords yet again puts the Tory Party’s interests before the public’s.
“This underhand attempt to game the system by installing a conveyor belt of cronies and skewing Parliament in the Tories’ favour for decades to come should never see the light of day. Rishi Sunak should make it clear in no uncertain terms that he will refuse to do Boris Johnson’s bidding and reject his disreputable demands.”
But Downing Street indicated Mr Sunak would not be intervening.
“There’s a long-standing convention that Prime Ministers do not seek to intervene in former prime ministers’ resignation honours lists, that’s been a case under successive governments,” the Prime Minister’s official spokesman said. “The Prime Minister is of the view that he will approach it as has been the case of successive governments.”