Jones has been available for employment since parting ways with Southampton in February.
His tenure with the Saints was relatively short-lived. He succeeded Ralph Hasenhuttl last November on a three-and-a-half-year deal.
However, he picked up just one league victory in eight matches and left the club languishing at the bottom of the league table.
This made him the shortest-serving non-caretaker manager in Southampton’s history.
Gary Rowett vacated his role as Millwall manager just two weeks ago. He had been in charge of the Championship club for four years.
Many people were taken aback by his departure, especially with Millwall only three points adrift of the Championship play-off positions at the time.
Rowett said the time was right to part ways and left Millwall in 15th place in the table after 11 league games.
Other contenders remain in contention for the role, with additional interviews scheduled for this week, but Jones is a front-runner for the job.
Rumours swirled linking Kevin Muscat and John Eustace to the position, but their appointments seem unlikely.
Michael Beale’s name has also been mentioned as a potential candidate following his recent departure from Rangers.
The Millwall board faces a critical decision as they look to fill the managerial void left by Rowett.
Jones’ impression on the club executives and his experience managing in the Championship makes him a compelling choice for the role.
The outcome of Millwall’s deliberations remains to be seen, but a decision will be announced soon.
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