What is the word that means to offer to be in a relationship?

There is a word that means to offer to be in a relationship. For example, it could be used in the following dialogue:

A: Let's go over to my apartment.
B: Are you [] me?

However, I can't think of this word. Any help?

Solution 1:

The first word that springs to mind is proposition, as in

Are you propositioning me?

That would generally imply sex rather than necessarily a longer relationship, but that would seem to fit your example dialogue :-)

Other possible words include: seduce, woo, pursue.

Solution 2:

I usually use: Are you hitting on me? :-)

Solution 3:

For an option which is slightly less sexual than proposition or hitting on, you might say:

Are you coming on to me?

Where to come on to someone means to flirt and entice someone, without necessarily implying that you're asking for a sexual act, which is what to proposition implies.