Reports suggest leader Ed Miliband has ruled out bringing back Labour veterans such as the Hull West and Hessle MP, who served briefly as shadow chancellor in 2010.
A former Labour minister told a national newspaper: "Successful political parties, such as successful businesses and successful sports teams, need a mixture of youth and experience.
"We need to show the voters we have a bit of gravitas, which is something we're lacking at the moment. Alan would be ideal but Ed simply will not do it."
Another senior Labour source said: "There will be no return of the greybeards.
"Ed wants to put across a message of change as we head for 2015."
Mr Johnson, who held several cabinet positions under Tony Blair and Gordon Brown, has been a regular recent guest on the BBC current affairs programme This Week.
He also recently published a memoir of his London childhood, called This Boy.
Mr Johnson has also been at the centre of regeneration plans for the Hull and Humberside area and spoke (along with former Labour leadership hopeful David Milliband)at the recent Yorkshire International Business Convention held at Bridlington Spa. One prominent local businessman said: "Alan Johnson is passionate about this area and has been at the heart of promoting the Hull City Plan to a wider audience and to creating relationships across the Humber. "It is faintly ridiculous to not consider him for the Shadow Cabinet but that will be Labour's loss and our gain".
