Throughout his career, the 6'0" Dillard profiles as an above-average three-point shooter, and reliable at the free-throw line.
Dillard's arrival would force Stockton out, with Carter and Akil Mitchell filling out the other import spots on the roster.
If Stockton is to be replaced, it would be a relatively recent decision.
The diminutive ball-handler aggravated a back injury in a game against Sydney Kings, but initially was set to make the trip to Cairns for tomorrow's clash with the Taipans.
"The initial response after the Sydney game was he could be a couple of weeks," Breakers coach Paul Henare said earlier this week.
"He seems to have freed up this week, and he got through training OK today. We'll take him up there and see how he goes."
Stockton averaged nine points and 4.3 assists per game on 38 percent shooting in nine games for the Breakers.
Earlier today, Corey Webster was ruled out for the season after deciding to undergo surgery, while Woodside (longterm) and Tom Abercrombie (2-3 weeks) are also sidelined.