Davids played in the club’s 4-1 pre-season friendly win over USA champions LA Galaxy and is hopeful of winning a contract with the Oregan club.
The 26-year-old is nearing the end of his contract in Belgium and has made no secret of his desire to leave the club.
With the transfer window still open in the USA ahead of the new season, he could make the move now if Portland Timbers decide they like what they see. Lierse have also confirmed that they will allow him to leave.
“We were asked whether the player could play in a friendly against Los Angeles and we gave permission for it. It is now up to Portland to decide whether they want to sign the defender or not,” Lierse technical director Ruud Kaiser said.
Portland Timbers will become the 18th side in the MLS after joining the competition in 2012.
They are managed by former Chelsea and Everton forward John Spencer, a Scottish international who finished his career with the Colorado Rapids in the USA in 2004.