As the No. 2 overall pick in the 2008 draft, Beasley had a hefty qualifying offer of $8.1 million to retain his rights. In two seasons with the Wolves, he showed flashes of the scoring ability that made him such a promising prospect at Kansas State. But a multitude of injuries and an inability to prove to coaches that he could be relied upon on a nightly basis has him looking for a new home again.

Beasley came to the Timberwolves on July 12, 2010 that helped the Miami Heat clear enough room to sign LeBron James and Chris Bosh. Wolves president David Kahn's investment was minimal -- a pair of second-round draft picks -- for a versatile forward with the ability to score inside and out.

The trade had the makings of a steal early in Beasley's stint with the Wolves, averaging 31.3 points over a six-game stretch in October and scoring almost 23 points a game in his first two months with the team. But ankle injuries slowed his first season in Minnesota and he averaged a career-low 11.5 points while dealing with a multitude of injuries last year under Rick Adelman.

"He's one of the best young talents that we have in this game, but he has the potential to be a great player," Miami guard Dwyane Wade said during the season. "If he wants it or not, that's what we always told him in Miami. We'll see."

That's always been the question with Beasley, and Adelman and the Timberwolves appear to have grown impatient waiting to find out the answer. He was moved to a sixth man role that took some time for him to get adjusted to, but Beasley was never able to put it all together last season.

"This year, I don't know why, but his offensive game wasn't there at the start but I at least thought he was trying defensively and just applying himself with more rigor than he had the year before with the previous staff," Kahn said in April. "And I was at least hopeful that maybe there is something here, and he got hurt again, and again.

He was very popular with teammates and never a problem in the locker room, but Beasley was cited for marijuana possession in June 2011. Still just 23 years old, he should have some suitors when free agency opens on Sunday, but not at the high salary he initially may have hoped for.

Beasley became the second player in the top three picks of the 2008 draft -- joining Memphis guard O.J. Mayo -- to be allowed to become restricted free agents when their teams did not make qualifying offers.

Randolph was the 14th overall pick by Golden State in that draft, and has bounced around even more than Beasley. He played sporadically last season for the Wolves, averaging 7.4 points and 3.6 rebounds and sometimes frustrating the coaching staff with his work ethic. But several members of the staff are intrigued by his athleticism, and Randolph could return to the team if he is willing to accept a salary much lower than his $4 million qualifying figure.

The Timberwolves also extended the deadline to reach buyout agreements with veterans Martell Webster and Brad Miller on Saturday. The extensions allow the team to continue trying to package them in trade deals to land a big man or a shooting guard, the team's two biggest needs.

Miller said at the end of the season that he will retire, but he is still on the books for $5.1 million next season. The deal could be bought out for much less, which makes him an attractive trade chip.

The same goes for Webster, who has been hampered by back injuries the last two seasons. He is due to make $5.7 million next season, but any team with his contract can buy him out for about $600,000.