Beyond raw materials and safe passage, Russia has little to offer.
That's why most cooperation to date has been limited to the energy sector.
For its part, China would have little to gain from binding itself to the Eurasian union's higher tariffs and rules.
Investment is another avenue for deeper integration.
But the union and members of the Shanghai group do not overlap neatly.
The recent admission into the group of Pakistan and India, two countries with high tariffs and political tensions, makes a free-trade zone even more unlikely.
Rhetoric about "linking" the BRI and Eurasian union mainly serves political objectives, but will struggle to produce concrete economic results.
Consider a few avenues for greater economic integration.
Putin's Eurasian Economic Union aims to integrate Russia and four former Soviet States in a single market for goods, services, capital and labor.
In July, Russia and China launched a feasibility study to "inject new strength for the comprehensive strategic partnership of the two countries."At first glance, these visions might appear complementary.
Moscow dominates the Eurasian union in economic and political terms, and admitting China would undercut that influence.