"What attracts me" is correct. For example: What attracts me to your suggestion is the idea that we will both profit. The past tense: What attracted me to your suggestion is the idea that we would both profit. In the above example "would" can be replaced with "could".

It's the normal conjugation of verbs in English. I attract You attract (singular) He/She/It attracts You attract (plural) We attract They attract In your example "what attracts me" is talking about "it". Other random examples: To manage - I/You/We/They manage , but He/She/It manages To put - I/You/We/They put, but He/She/It puts some irregular examples (because it introduces an e into the verb), but following a similar pattern: To go - I/you/we/they go, but He/She/It goes To do - I/you/we/they do, but He/She/It does