Let \(R\) be an associative ring. A left \(R\)-module \(_RW\) is said to be cotilting if the class of modules cogenerated by \(_RW\) coincides with the class of modules for which the functor \(\text{Ext}^1_R(-,W)\) vanishes. This paper explores the relation between cotilting modules and pure-injective modules. In fact, by a more recent result of \textit{S. Bazzoni} [Proc. Am. Math. Soc. 131, No. 12, 3665-3672 (2003; Zbl 1045.16004)], every cotilting module is pure-injective. Therefore, the results obtained in this paper for pure-injective cotilting modules are actually valid for all cotilting modules. Among them is the fact that if \(_RW_S\) is a cotilting bimodule, then \(R\) and \(S\) are semiregular rings and also the characterizations given of reflexive modules in terms of linear compactness conditions.