Sources said Saturday that the Spurs have made the strongest pitch among the various playoff contenders chasing Martin, who has been in advanced negotiations on a contract buyout with Minnesota.
Martin and the Timberwolves have until midnight ET Tuesday to part ways in order for Martin to be playoff-eligible for his next team.
The Cleveland Cavaliers, Dallas Mavericks and Houston Rockets, sources say, are also among the known suitors for the 12-year veteran, who has averaged 17.6 points in 30.5 minutes per game in his career.
Martin is an established scorer who instantly became an appealing target for a number of playoff-likely teams once his name surfaced on the buyout market after staying put at the trade deadline.
On Thursday, the Wolves bought out another veteran guard -- Andre Miller -- to free the 39-year-old to seek employment with a playoff-hopeful team. Miller cleared waivers Saturday and his agent said he would sign with the Spurs.
Like Miller, Martin has been used sparingly this season by the Wolves, who have fully focused on developing their young players in the wake of their inability to build on an 8-8 start. But the 33-year-old long has been regarded as a high-efficiency player with a propensity to get to the free throw line. He's also a lifetime .385 shooter from 3-point range.