NewsAtDen understands that boss Kenny Jackett is keen to see the right-back, 25, in action and has invited him to begin training with the Lions next week.
Moutaouakil, who was released by Charlton in 2010, is currently plying his trade with Conference South outfit Hayes & Yeading.
He has had unsuccessful trials at Swansea City and Oldham in recent years after a rapid fall from grace.
Charlton reportedly beat off competition from Everton, Aston Villa, Celtic and Lazio to sign Moutaouakil for £400,000 in the summer of 2007.
Born in Nice, Moutaouakil began his career at Ligue 2 club Châteauroux and went on to make five appearances for France's U21 side, once as captain.
But he struggled to settle at The Valley and was allowed to join Portsmouth on trial in 2009, before being loaned to Scottish side Motherwell during the 2009-10 season.
Millwall are well-stocked defensively, with incumbant right-backs Alan Dunne and Jack Smith both under contract for two more years, but Jackett is prepared to give Moutaouakil a chance to impress.