It is believed Mr Alexander is planning to stand as an MP for Labour at the next general election.
He is understood to have submitted his application to be the party’s candidate in East Lothian in a move that could pit him directly against incumbent and Alba MP Kenny MacAskill.
Journalist and broadcaster Michael Crick wrote on Twitter: "I understand former Cabinet minister Douglas Alexander has submitted his application to be Labour candidate for the dual East Lothian/Midlothian selection."
Mr Alexander left politics after dramatically losing his Paisley and Renfrewshire South seat to the SNP’s Mhairi Black, then just 20, at the 2015 election – a vote that left Labour with only one MP in Scotland in Ian Murray.
If re-elected, Mr Alexander would bring experience to a potential Labour Government, with only two shadow cabinet members – Yvette Cooper and Ed Miliband – having previously held Cabinet roles.
Mr Alexander has been a senior fellow at Harvard University since his tenure ended as an MP.
The brother of former Scottish Labour leader Wendy Alexander, he was elected MP for Paisley South in 1997 and served as Labour's campaign co-ordinator at the 2001 general election before getting his first ministerial role in charge of e-commerce.
He later served as transport and Scottish secretary and then international development Secretary.
East Lothian looms as Labour’s primary target in Scotland. The seat was held by Labour until 2015, when it went to the SNP before Labour took it back in 2017.
The current MP, former justice secretary Mr MacAskill, won the seat for the SNP again in 2019, ousting Labour's Martin Whitfield, but Mr MacAskill has since defected to Alba.
There are said to be mixed feelings about the prospect of Mr Alexander as Labour's candidate.
One Labour source said earlier this month: "Some folk are saying he's had his turn and it's time for a fresh face. They argue Labour needs a new, younger generation of MPs. And they're wondering why Douglas isn't going after one of the Paisley seats, where he has connections."
Labour opened its process for candidate selection for East Lothian last week.
Katherine Sangster – an aide to Mr Murray – and activist and communications specialist Gregor Poynton are tipped to also submit their names.