Recommending the identity of bidders in public procurement auctions has a significant impact in many areas of public procurement, but it has not yet been studied in depth. A bidders recommender would be a very beneficial tool because a supplier can search appropriate tenders and, vice versa, a public procurement agency can discover automatically unknown companies which are suitable for its tender. This paper develops a pioneering algorithm to recommend potential bidders using a machine learning method, particularly a random forest (...) classifier. The bidders recommender is described theoretically, so it can be implemented or adapted to any particular situation. It has been successfully validated with a case study: an actual Spanish tender dataset which has 102,087 tenders from 2014 to 2020 and a company dataset which has 1,353,213 Spanish companies. Quantitative, graphical, and statistical descriptions of both datasets are presented. The results of the case study were satisfactory: the winning bidding company is within the recommended companies group, from 24% to 38% of the tenders, according to different test conditions and scenarios. (shrink)