  Based on the nonrelativistic QCD framework, we study the $\Upsilon$
production in semi-inclusive deep inelastic electron-proton scattering (SIDIS)
at HERA, EIC, and LHeC, with the main aim of assessing the viability of
observing $\Upsilon$ electroproduction at the three colliders. The color-octet
(CO) contributions are found to have a crucial effect on both the integrated
and differential cross sections, serving to further establish the significance
of the CO mechanism. By setting the kinematic cuts to $p_{t,\Upsilon}^{\star
2}>1~\textrm{GeV}^{2}$, $W>50$ GeV, $2<Q^2<100~\textrm{GeV}^2$, and
$0.3<z<0.9$, only a few electroproduced $\Upsilon$ events can be generated at
HERA, partially accounting for its lack of measured $\Upsilon$
electroproduction. However, under the same cut conditions, the EIC and LHeC can
accumulate about $8.7\times10^{2}$ and $3.7\times10^{4}$ reconstructed
$\Upsilon$ events in one operation year, respectively, which manifestly
indicates the prospect of detecting the $\Upsilon$-related SIDIS processes at
the two forthcoming $ep(eA)$ colliders.
