Albanian is not a Romance language but has a large Latin vocabulary. It also shares, along with Romanian (also Bulgarian and Macedonian), the core features of the Balkan Sprachbund.
Dan Alexe in Dacopatia şi alte rătăciri româneşti (part of that here) argues that beside the few tens of terms only common to Albanian and Romanian, Albanian has a Latin vocabulary that is not only comparable in number to the Romanian, but is also common to Romanian. He also argues that many Latin, Slavic and other words common to both languages have been transformed in the same way in both, and according to the same rules.
Funny enough (but also interestingly) he mentions many Romanian terms normally marked as having unknown origin which can be explained through Albanian — e.g. bordei (small village house with an underground chamber), from borde ("hole" in Albanian); the odd Romanian expression eu unul, which means in fact "as for me", but very unusual for Romanian (literally "I the one"), from Albanian
üne which means "I"; the odd form of the first person singular of "to have" in Romanian, eu am (I have) is explained through the influence of the Albanian kam (meaning "I have"). Etc.
From the Albanian point of view, Romanian is close, given no closer related languages survive. From the Romanian point of view, other languages (the other neo-Latin languages) are obviously closer relatives than Albanian, that is, considering the entire family of Romance languages. But that being said, and considering only the area of Eastern Romance, Albanian is close even if it is not part of the Romance family: essential features of Eastern Romance are only present in Romanian and Albanian. (At the same time these features are connected to those that define all members of the Balkan Sprachbund).
That doesn't make the two languages closely related, but makes them at least relatively close.