In contrast to symbol-manipulation approaches, Cognitive Linguistics offers a modal rather than an amodal account of meaning in language. From this perspective, the meanings attached to linguistic expressions, in the form of conceptualisations, have various properties in common with visual forms of representation. This makes Cognitive Linguistics a potentially useful framework for identifying and analysing language-image relations in multimodal texts. In this paper, we investigate language-image relations with a specific focus on intersemiotic convergence. Analogous with research on gesture, we extend the notion of co-text images and argue that images and language usages which are proximal to one another in a multimodal text can be expected to exhibit the same or consistent construals of the target scene. We outline some of the dimensions of conceptualisation along which intersemiotic convergence may be enacted in texts, including event-structure, viewpoint, distribution of attention and metaphor. We take as illustrative data photographs and their captions in online news texts covering a range of topics including immigration, political protests, and inter-state conflict. Our analysis suggests the utility of Cognitive Linguistics in allowing new potential sites of intersemiotic convergence to be identified and in proffering an account of language-image relations that is based in language cognition.