The Detroit Pistons center is a restricted free agent.
The Detroit Pistons have the option of matching any contract offered by another team, but they could be forced to trade him if Monroe makes it clear he wants to be in Portland.
The Trail Blazers do not have the cap space to sign Monroe outright, but they have assets that could interest the Pistons, such as swingmen Wesley Matthews and Nicolas Batum.
ESPN's Mark Stein tweeted that the Blazers were seriously interested in trading for Monroe.
Another team to watch in the Greg Monroe restricted free-agent hunt: I'm told Portland has serious interest in a sign-and-trade for Monroe— Marc Stein (@ESPNSteinLine) July 1, 2014
Stein also reported that the Orlando Magic and Atlanta Hawks are potential suitors for Monroe, and both have enough cap space to potentially sign him outright if the Pistons decide not to match.
Monroe would be an intriguing fit for the Trail Blazers, who are coming off the back of a good season in which they made the second round of the playoffs.
In Damian Lilliard and LaMarcus Aldrige Portland have two stars, and a third big piece could push them to the point where they could win the Western Conference.
Robin Lopez game them some decent production at center last season but Monroe is a clear upgrade at the five. He's a very good all-around player, a solid rebounder and good scorer in the low post.
The Trail Blazers have also expressed interest in signing Spencer Hawes, who is currently an unrestricted free agent. Adrian Wojnarowski tweeted that the team met with the center in Los Angeles when free agency opened.
Portland GM Neil Olshey met with free agent Spencer Hawes and his agent, Greg Lawrence, tonight in Los Angeles, sources tell Yahoo.— Adrian Wojnarowski (@WojYahooNBA) July 1, 2014
Hawes would be another good fit for Portland with his rebounding and shooting ability from anywhere on the floor.
Chris Haynes of CSNNW.com reports that Lillard was asked by text message if there were any free agents he would like the team to target. His first preference was Portland's Mo Williams, but from other teams he wants the Trail Blazers to pursue Hawes, Channing Fry, Vince Carter and Trevor Ariza.