HEY GURL HEEEY!!!! How are you doing bunny !?
I think it may be possible if it was someone he knew before he turned himself into a puppet or if he linked a certain (special) emotion or event to that person (that requires him knowing the person beforehand too, right?). Maybe if the persons character was what Sasori considers pleasant.
unlike deidara.He might also build a connection to a person if they share the same or a similar view on art.
I think it may be not as hard to talk about his past for him than you think. Sasori already kind of accepted his parents absence when he was a child. I imagine if someone would ask him about what he did before he joined akatsuki and what his past was like he will just plainly give them the facts. Not in detail though. He would mention that his parents died pretty early, he left the village and then joined the akatsuki or whatever. BUT I’m certain that he would never ever discuss his actual feelings (especially about his parents) with someone. It’s the fact that he has locked up all of his feeling pretty tight. He would say he has none, but he really just has locked them up. He know they are still there, but will refuse to lett them out at all costs. It’s not like he has the urge to do so anyway. Thus he will never ever talk about his feelings with someone, because he insists he has none.
So yes, I think there a few ways that will get him to warm up to a person and maybe he will even take a liking to that person, but I wouldn’t say he is able to fall in love. One factor might be that he probably doesn’t know or rather forgot how love feels and looks like.
WHYYY don’t get me started on sasori omfg
but I hope this is a satisfying answer bb