Last week, he told me that by the end of the next term, he __________(develop) his interest in memorizing words for more

Last week, he told me that by the end of the next term, he __________(develop) his interest in memorizing words for more than 3 months.
空格不限词数,请填入develop的正确形式.本人认为可用过去将来完成时,或者过去将来完成进行时,不知道您怎么看?请分析并解释一下,谢谢!