than me、than I、than I am 都可以。

【这是Oxford Dictionary of English 3rd ed. 对 than 一字的附加解说】
– origin Old English than(ne) , thon(ne) , thænne , originally the same word as then .
/usage: Traditional grammar holds that personal pronouns following than should be in the subjective rather than the objective case: he is smaller than she rather than he is smaller than her . This is based on an analysis of than by which than is a conjunction and the personal pronoun (‘she’) is standing in for a full clause: he is smaller than she is . However, it is arguable that than in this context is not a conjunction but a preposition, similar grammatically to words like with , between , or for . In this case the personal pronoun is objective: he is smaller than her is standard in just the
same way as, for example, I work with her is standard (not I work with she). Whatever the grammatical analysis, the evidence confirms that sentences like he is smaller than she are uncommon in modern English and only ever
found in formal contexts. Uses such as he is smaller than her , on the other hand, are almost universally accepted. For more explanation see usage at personal pronoun and between .

than me比较常见 是口语里面弱化第一人称的用法
than I am 是书面用语

都行