BRUSSELS—The European Union could significantly scale back sanctions and resume discussions with Russia on issues ranging from visa-free travel; cooperation with the Moscow-led Eurasian Economic Union; and the crisis in Libya, Syria and Iraq; if Russian President Vladimir Putin moves to end the crisis in eastern Ukraine, according to an EU discussion paper.

While insisting the EU can’t return to “business as usual” with Moscow, the paper suggests the EU consider gradually normalizing many aspects of its ties with Russia in...