"It's all but done. It's a good deal. We're just trying to work out the final details, but I can't imagine it won't happen at this point," American newspaper, The Washington Post, quotes a source as saying.
Convey is believed to have been offered a four-year contract with Spurs and the only thing holding-up the deal is Spurs gaining a work permit for the 20-year-old.
"We are actively involved in obtaining a work permit," Dan Segal of SportsNet LLC, which represents Convey, told the Post.
"However, nothing is guaranteed and the deal can't go through without it."