This paper focuses on a specific instrument which may help prevent algorithmic discrimination in contractual relationships: fundamental rights impact assessments. The first fundamental rights impact assessment model considered in this paper is the one prescribed by article 27 of the EU AI Act. This impact assessment is mandatory not only for public bodies but also for several categories of private actors. The second model addressed in this paper is the Fundamental Rights and Algorithms Impact Assessment (FRAIA), developed in the Netherlands a few years ago to prevent violations of fundamental rights through algorithms. The paper then addresses some examples of algorithmic discrimination in contractual relationships and concludes by questioning the capability of fundamental rights impact assessment systems to prevent algorithmic discrimination by powerful contract parties in the EU.