  We investigate the potential of the process $gg \to H \to WW$ to provide
bounds on the Higgs width. Recent studies using off-shell $H\rightarrow ZZ$
events have shown that Run 1 LHC data can constrain the Higgs width, $\Gamma_H
< (25-45) \Gamma_{H}^{\rm SM}$. Using 20 fb-1 of 8 TeV ATLAS data, we estimate
a bound on the Higgs boson width from the WW channel between $\Gamma_H <
(100-500) \Gamma_H^{SM}$. The large spread in limits is due to the range of
cuts applied in the existing experimental analysis. The stricter cuts designed
to search for the on-shell Higgs boson limit the potential number of off-shell
events, weakening the constraints. As some of the cuts are lifted the bounds
improve. We show that there is potential in the high transverse mass region to
produce upper bounds of the order of $(25-50) \Gamma_H^{SM}$, depending
strongly on the level of systematic uncertainty that can be obtained. Thus, if
these systematics can be controlled, a constraint on the Higgs boson width from
the $H \to WW$ decay mode can complement a corresponding limit from $H \to ZZ$.
