Parker "should be ready" to play in Game 1, two sources with direct knowledge told Yahoo Sports.
Parker will work to rehabilitate the sprain over the next several days of preparation for the Finals rematch with the Miami Heat.
Parker had been bothered by the ankle since Game 4 of the Western Conference finals and tried to play on it in Game 6 before missing the second half of the clinching victory over the Oklahoma City Thunder.
Parker has averaged 17.8 points and five assists in the playoffs.
Without Parker, the Spurs managed to cobble together a second half and overtime with Cory Joseph and Manu Ginobili playing point guard and still beat the Thunder.