Sources told ESPN.com that a deal with Jackson is on course to be finalized this week, potentially before the Clippers visit the Boston Celtics on Wednesday night in coach Doc Rivers' first game there since leaving the Celtics in June to take over in L.A.
ESPN.com reported earlier Monday that Jackson had emerged as a prime candidate for the Clippers to sign in the wake of several injuries that have decimated L.A.'s depth at the wing positions.
On Sunday night, Jackson cryptically tweeted: "I never lost faith. The wait is over."
Jackson, 35, has been searching for a new team since his sudden release by the Spurs shortly before last season's playoffs in April. Injuries suffered by starting guard J.J. Redick, top reserve Matt Barnes and rookie forward Reggie Bullock prompted Rivers to announce after Saturday's loss in Cleveland that the Clippers essentially "have to look somewhere" for reinforcements.
Asked about Jackson before Monday's game, Rivers said: "We are close. It's not done yet. Nothing's done in our league until it's done. I just think he's a veteran. We need him in a pinch. We need him like now and that's a guy that you can bring in and he can give you something right away with Reggie being out for at least this trip and maybe longer and Matt being out. We don't have another three right now and he fits that bill for us."
Former Los Angeles Lakers and Phoenix Suns guard Shannon Brown has also been mentioned as a potential target, but Jackson has the sort of size, 3-point shooting range and playoff résumé that is said to appeal to Rivers as the Clippers search to fill the void.
It was not immediately known how the prospect of a signing this week, if it indeed goes through as expected, would impact the Clippers' well-chronicled interest in re-signing veteran forward Lamar Odom.
Rivers has spoken optimistically in recent weeks about Odom's chances of returning to the Clippers after a tumultuous offseason, but the mounting injuries have left L.A. with a more pressing need than Odom might be able to fill.
Another possibility is that the Clippers sign Jackson this week to fill their one open roster spot and then release another player later to make room for Odom, who sources say is making good progress in his personal workouts in preparation for a return to the NBA that is now widely seen as inevitable.
Redick is out at least six more weeks with a fracture in the small bone in his right hand and a tear of his right ulnar collateral ligament. Barnes has been plagued by a torn retina in his left eye that has already required two surgical procedures. And Bullock suffered a suspected high ankle sprain in the loss at Cleveland.
Jackson, meanwhile, has been working out on his own in Texas in hopes of hooking up with another contender.
Spurs coach Gregg Popovich abruptly released Jackson in April just six days before the end of the regular season because the Spurs felt that he was unwilling to accept a lesser role in the playoffs behind fast-developing youngsters Kawhi Leonard and Danny Green. Jackson later said in numerous interviews that he actually asked the Spurs to move him before the league's annual trade deadline in February but couldn't convince them to go along with the request.
ESPNLosAngeles.com's Arash Markazi contributed to this report.