The Frenchman has been without a club since leaving German side Werder Bremen in the summer and spent time training with Sir Alex Ferguson's side in October.
Timbers club owner Merritt Paulson confirmed that the 35-year-old was expected to start training with the club.
"Look forward to seeing Mikael Silvestre in Timbers green at training today (Tuesday)," Paulson wrote on his Twitter page.
Silvestre, has not played a competitive match since January 2012 but could become the latest Premier League player to move to America, following Robbie Keane and Thierry Henry to the MLS.
Portland Timbers finished eighth in the Western Conference last season.