A copy of the investigation's file seen by Reuters showed those under investigation include current Leonardo Chief Executive Alessandro Profumo and the current Chairman of Banco BPM Massimo Tononi.
Both Profumo and Tononi in the past chaired Monte dei Paschi's board of directors.
The prosecutors said in the statement they were not requesting a trial for Monte dei Paschi. This is expected to lead to charges against the Tuscan bank being dropped.
Prosecutors have been looking into allegations of false accounting and market manipulation in relation to the classing of loans as impaired at Monte dei Paschi up to 2017.
Lawyers for Profumo and Tononi and the other two people did not immediately reply to a request of comment from Reuters.
A judge will decide on the request for trial at a hearing in the near future. Normally such requests lead to a trial.
(reporting by Emilio Parodi, writing by Valentina Za, editing by Gavin Jones)
