The former Manchester United and England defender, who was previously coach of Inter Miami before losing his job shortly before Lionel Messi's arrival at the club, said the Timbers were looking to bring in an elite player.
MLS's rules allow teams to sign up to three 'designated players' whose salaries do not count fully against the team's salary cap.
The rule was brought in to allow Los Angeles Galaxy to sign Neville's former teammate David Beckham in 2007 and Messi is the biggest name 'DP' to have joined the league.
"We've got ownership's backing to go out there and bring in a top, top DP," Neville told MLSSoccer.com.
"I think over the next two or three weeks, there will be some exciting news coming our way," he added.
The Timbers have cleared space for a new DP by declining a contract option on Polish striker Jaroslaw Niezgoda and selling Colombian winger Yimmi Chara.
Portland currently have one DP, Brazilian midfielder Evander so a striker would be the most likely new arrival.
Neville suggested there could be a number of new faces joining the club in the coming weeks.
"You look at the money that's been spent around, particularly the Western Conference and the Eastern Conference now, you need to get these signings right," he said.
"That means you've got to do your due diligence, your scouting, your recruitment. That's what we're doing," he added.
The Timbers won MLS Cup in 2015 and were beaten finalists against New York City in 2021 but did not make it to the playoffs last season after finishing tenth in the Western Conference.
