A person familiar with the situation confirmed they were close to a deal for Beasley after trying to involve Portland as a third team.
"They're pushing for it," said the source, who requested anonymity because he was not authorized to comment publicly.
The second pick in the 2008 draft, Beasley is averaging 11.8 points and 4.6 rebounds in the last year of his contract. He has become expendable in Minnesota because rookie forward Derrick Williams is getting more time.
Beasley, 23, is listed at 6 feet 10 and can play both forward positions.
In one scenario, Lakers back-up point guard Steve Blake would be sent to Portland. The Trail Blazers would then deal Jamal Crawford to Minnesota. A draft pick and another lesser player might be involved as well.
"I'm still here," Blake said in the Lakers' locker room before their game Wednesday against New Orleans. "I'm just getting dressed and ready for the game."
The trade deadline is Thursday at noon Pacific time.
If the Lakers lose Blake, they will turn their attention rapidly to Cleveland point guard Ramon Sessions. The Lakers still have a $9-million traded-player exception that could net Sessions for a draft pick.
Sessions, 25, is on the market because the Cavaliers have handed their offense to rookie point guard Kyrie Irving. He is averaging 10.7 points and 5.2 assists in 24.6 minutes as a reserve. He has one more year on his contract for $4.6 million.
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