Burke could make his major-league debut Tuesday against the Angels, Jeff Wilson of the Fort Worth Star-Telegram reports.
The Rangers are scheduled to play a doubleheader Tuesday, so Burke may be recalled to toe the rubber for one of the two matchups. He's spent the majority of his time with Double-A Frisco this season, posting 3.18 ERA and 1.02 WHIP with a 49:12 K:BB over 45.1 innings.