According to the report, the fee could rise to £12m with add-ons for the centre-back, who the Catalans recently recalled form a loan spell at Ligue 1 side Nice.
The Brazilian initially joined Barcelona on loan from Fluminense in his homeland, predominantly featuring for Barca's 'B' team.
However, with the club looking to cash in on their fringe players this summer, he has been made available for transfer, with Mark Hughes keen as he looks to ensure he has the personnel available to continue to play with the three at the back system that got the best out of his side last season.
A Brazil U20 international, Marlon is highly-rated in his homeland and 'Saints' hope to add him to their ranks ahead of getting the new Premier League season underway against Burnley on August 11.