I understand that I am taking risk, but there are no such known sources. Let someone prove me wrong. And even in Slavic languages, the Chronicle that you mention seems to be the only source.
Of course the expression "rulers of Russia" that you use, is an anachronism. There was no "Russia", and those Varangian leaders of the time of Rurik did not rule any substantial territory.
Some Islamic and other sources mention a "Kahan of Rus", and some Western sources mention people who came from Constantinople and call themselves Rus, and who were actually Swedes.
("Rus" in these sources is an ethnonym, not a geographic name.) But there are no sources mentioning Rurik, Oleg, Askold or Dir.
Archeology shows that there were Scandinavian settlements in the regions of Novgorod, Kiev and elsewhere.
Byzantine sources show that they attacked Constantinople several times: first time in 860 with unidentified leader, second time in 940 by Igor with whom they concluded a treaty 3 years later. This treaty is preserved in the Chronicle.
The next ruler name from the Chronicle which is confirmed by Byzantine sources is Olga (the wife of Igor who was Rurik's son according to the Chronicle). She visited Constantinople and her visit is recorded by Byzantine historians.