Rubin, in the Russian republic of Tatarstan, is the furthest east of any European club in the competition but they played their last-16 home match against Levante at Moscow's Luzhniki Stadium due to problems with the pitch.
A decision on where to play the Chelsea game on April 11 is due later on Friday, but that too is expected to be in Moscow. It would mean a shorter journey - though still a significant one - for Rafael Benitez's team ahead of a possible FA Cup semi-final three days later.
In the other Europa League quarter-finals, Tottenham appeared to be handed the easiest draw after being paired with Swiss side Basle, while Newcastle will play Benfica from Portugal and Turkish side Fenerbahce will face Lazio of Italy.
Rubin Kazan will be tough opponents for Benitez's Chelsea team.
The Russian side have already knocked out two Spanish teams - holders Atletico Madrid in the round of 32 and Levante on Thursday night, winning 2-0 after extra time.
Rubin were also unbeaten in a tough group that include Inter Milan and are particularly strong defensively, having conceded only three goals in 10 European matches. Spurs' opponents Basle scraped into the quarter-finals after Russian side Zenit St Petersburg missed a late penalty against the 10-man Swiss side.
Newcastle's opponents Benfica came into the Europa League knock-out stages after finishing third in a Champions League group including Celtic and Barcelona, during which they achieved a 0-0 draw at the Nou Camp.
Former Newcastle and Holland striker Patrick Kluivert, who carried out the draw for UEFA, said he believed an English side has a great chance of winning the competition.
Kluivert said: "There are three great teams from England, Chelsea, Tottenham and Newcastle and for sure one of those can lift the trophy but there will be other teams eager to do so too so that can only be good for the competition."