Morales made a spot start in place of Josh Beckett on Sunday against the Twins, pitching six dominant innings in a 6-4 victory.
Manager Bobby Valentine's preference for a while has been to start Morales, but there haven't been any rotation vacancies.
Aaron Cook, who had struggled in three straight starts before pitching well in his most recent start, would be the most logical candidate to get bounced from the rotation. But Valentine said earlier this week that he will pitch in next week's three-game series in Baltimore.
Expect Valentine to reveal his pitching plans in more detail over the next couple of days.