Whether bilinguals perform better than monolinguals in non-linguistic cognitive control tasks is a matter of current debate. Bilinguals are constantly required to switch and discriminate between their two languages. Such additional discrimination requirements are thought to result in improved domain-general cognitive control abilities compared to monolinguals. This rationale was examined by taking it one step further. A general link between general response selection (i.e., cognitive control mechanisms) and word selection should be apparent within the monolingual population, thus the natural variability present in response discrimination abilities should predict word selection in a population of monolinguals. A large group of young monolingual pupils were tested in the non-linguistic Simon task and in a picture naming word selection task. Selection difficulty was manipulated in both tasks. There were clear effects of response selection difficulty in either task, but there was no relationship between them at the individual level. This null effect provides no support for the hypothesis tested. It prompts a tentative discussion of exactly what process, in bilingual language use, may be capable of promoting cognitive control abilities.