Clearly as close to romantically as you can get without declaring an official relationship
They are not lovers. Allen, for one, still has misconceptions about the extent of her affection, judging by ch.27 p.10. He is a valued and trusted asset, he knows that much, and he might suspect there is a degree of affection from Ana, but the "romantically" part is not as "clearly" telegraphed by Ana, and is a moot point anyway, given
the nature of the relationship
who's basically already property of the family.
"Basically" does a lot of heavy lifting here. The Duke says that he can refer Allen to another employer if he so desires, implying he is not under serfdom or anything like that, and so Allen is a free man in an economic system not dissimilar to the contemporary job market. Whatever allegiances he has to the family, it is by his own will that he's their employee.
Actually, the "property" part is really fucking uncomfortable, and is the issue I have with Ana's attitude towards Allen, if that is indeed the cause of her treatment of him.
The dude already spends time with her in private
In the same way you would with your trusted servant. So far, every instance of them being together in private shown in the manga has been about her requiring his assistance in one way or another.
gets call her by a nickname, they're already making physical contact with each other, and hell, and unless there was a translation issue in the p.27, he even gets to bend the rules a bit when it comes by using said nickname in public.
Sounds like a big deal alright. Ana's been the one to make physical contact in form of an occasional shoulder pat or oh-so-appropriate face grab, Allen does not dare touch her in any way unless it is purely functional, like pulling her by hand to the adventurer guild hall in this chapter, so the part where
they're making physical contact is quite misleading.
Meanwhile, Allen's been
showering with the adventurer guild lady
Seriously, what do you expect the relationship to be when they specifically can't be an item?
To be a relationship where she respects his privacy and boundaries?
Brother, the very last page makes it clear the nature of the relationship, and how both parties are, and should continue to, take steps to not hurt each other, despite the obvious mutual attraction.
The last page is
his thought bubble about how
he shouldn't get his hopes up and try pursue realtionship with her. It is the line he draws, which also coincides with the line at which he is content with being hers, that is, protect and support her from the sidelines of his own drawing.
Ana being possessive of Allen achieves the opposite of preventing them from hurting one another, and, if she accepts the current status quo of Allen not being allowed to enter a relationship with her, is what I call "leading him on".