Albanian has no surviving immediate relatives, and in fact no known close relatives at all within the IE family. It constitutes a separate IE branch all by itself.
But, taking the terms "relative" and "closeness" in a more common or general sense, one could mention its relation to Romanian.
There is a specific Wikipedia article on Albanian–Romanian linguistic relationship:
Albanian and Romanian share most Balkan features, but they also have
common features which do not characterize other Balkan languages.
The Romanian philologist Bogdan Petriceicu Hasdeu who studied the
pre-Latin elements of the Romanian language came to the conclusion (in
1901) that the origin of the shared vocabulary was most probably to be
searched in the earliest phase of the two peoples' ethnogenesis... The
Albanian linguist Eqrem Çabej was the first to emphasize the similar
phonological and morphological elements of the two languages. He also
drew attention to the similarities between Albanian and Romanian
proverbs and the parallel development of the formation of sentences.
The Tosk dialect of Albanian, spoken in Southern Albania, in
particular is held to have experienced developments parallel to early
Romanian. ...The proposed interaction between Tosk and Romanian is
held to have been the last stage of the crucial Albanian–Romanian
period of convergence. Since these effects are marginal if present at
all upon Slavic loans, they likely occurred before contact with Slavs.
When comparing the morphological elements of the four core languages
of the Balkan linguistic area, scholars have concluded that Albanian
and Romanian share most common features.
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.
From the Albanian point of view, Romanian is close, given no closer related languages survive. From the Romanian point of view, other languages are obviously closer relatives than Albanian: first of all the other neo-Latin languages, then maybe South-Slavic languages like Bulgarian, given the large Slavic lexicon of Romanian. On the other hand, the common Slavic influence brings Albanian and Romanian close to each other too.
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.
Here is an article with a 17-page list of common words of the two languages (of various origins: substrate, Latin, Slavic etc): Common Lexic in Romanian and Albanian. Substrate and Loanwords, by Dan Ungureanu.
Here's a snippet:

Dan Alexe in Dacopatia şi alte rătăciri româneşti ("Dacopathy and other Romanian delusions" - 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 unu(l), which means in fact "as for me", but very unusual for Romanian (literally "I the one"), from Albanian üne which means "I". —The author tries also to explain the form of the first person singular of "to have" (eu am=I have) through the influence of the Albanian kam (meaning "I have"); but that form has to be related to the Slavic form of "I have" (Bulgarian, Serbian, Slovenian imam, Polish ia mam, Czech mám)—