Tanganga, 24, is poised to return from a disastrous loan spell at Augsburg after failing to make a single appearance for the German club.
The versatile defender, who can play across the back four, is now expected to link-up with the injury-hit Lions and could train with his new club as soon as Thursday.
Augsburg signed Tanganga in the summer on loan with an option to buy but injury and a change of manager meant he was was left well down the pecking order.
He is out of contract at the end of the season but Spurs have an option to extend his deal by a year.
Millwall have changed styles under new head coach Joe Edwards, appointed in November, and are now playing passing football, more in line with Spurs' style under Ange Postecoglou.
Edwards has said he needs more depth and wants to add more than one new player this month.
"We're not going to be spending millions, the club is really well and sensibly run financially but I definitely would love to strengthen," he said this week.
"I wanted to before but if you see our bench in the last few games, in this spell we've had with injuries... There's been certain games this season -- the last two, 'Boro and Leicester -- when on 60, 70 minutes and look along at the subs these teams are making you're reminded of the depth these teams have.
"We've been working hard, it's clear not easy but I would hope by the end of it there's some activity. I would hope we've done at least one or two by the end of the window.