They are both extremly close to each other as friend. The series has them quite close (one can assume they have feelings for each other).
Here's a Link with more Information and SPOILERS:
http://www.cracked.com/funny-6040-yugioh-gx/
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No.
It is implied that she does (for example in one episode Blair winks at Jaden and Alexis gets all mad) but it is never really confirmed and they never take their relationship past friends
No one knows for sure since it is not stated in the anime or manga. Many people think that it is hinted that he likes Alexis but it is never shown. In my personal opinion, all those "hints" were just Jaden being a friend, and I have seen him be closer to the guys then the others. So unless Jaden is actually gay somehow, he doesn't seem to like anyone.
Previous answer: its not proven but hinted in many episodes and in wiki!My Answer:Jaden does NOT love Alexis but, Alexis does love Jaden. Jaden is just dense (which was shown in many episodes) so he doesn't notice that Alexis is showing some affections or something like that. If Jaden wants a certain someone to be his he should've find a way to get her like knowing about relationships or what is love then he won't be dense. But in the manga both of them just show close friendship-ness but Jaden is still dense though.PS- There are NO hidden relationships, feelings or anything else similar to it in the GX since there is nothing shown. If there is, the creators would've told it or just post it into some website but if you support the fiancee-shipping, its alright to imagine that there is some hidden things. But still, the truth is the truth, right?
They only kiss in fan art