Recent technological advancements allow monitoring of drivers’ behaviour and offer the opportunity for providing feedback. While this approach has been shown to have a positive effect on driver behaviour, whether it is accepted by drivers has not yet been extensively investigated. This questionnaire study examined the opinions of a sample of 628 Dutch drivers on the potential use of a monitoring and feedback system. The focus was on (1) whether drivers would be interested in being assessed, (2) whether data collection (i.e., monitoring) could be used for this purpose, and (3) which features the potential system must have in order to get accepted. The results showed that participants were moderately enthusiastic about the prospect of receiving monitoring feedback: on average, their opinion was between neutral and positive. Professional drivers expressed slightly more positive opinions, but no demographic variable was strongly associated with acceptability. Many drivers rated themselves as good drivers already and had low sensitivity to data collection, i.e., participants indicated being used to data collection online. If they were to use a monitoring and feedback device, participants indicated a preference for data on speed and forward-facing video footage and a preference for personalisation. The use of a monitoring and feedback system can be considered as a trade-off between sharing personal data and receiving support to improve driving skills. Based on the participants’ reported online behaviour, it appears that the perceived costs associated with sharing data are small. The potential benefits of driver monitoring and feedback, however, are not salient to the participants, which may limit the use of such a system on the roads.