It happens in almost all Hollywood productions, before the director or the actors finish filming a movie, the processes of pre-production and casting give a thousand and one opportunities to other possible candidates. The same happened with the Matrix and Will Smith. We know who got casted and did an amazing job with the role, but we had no idea about what happened before Keanu Reeves.
Will Smith, soon to be the known mostly for his role as the genie in Aladding, recounts in videos being streamed from the Storytime series on YouTube. In this occasion, Will Smith explains in a very funny way how the Wachowski Brothers appeared to offer him the role of Neo in The Matrix.
Apparently, Smith, who explains that at that time the Wachowskis were simply known for the indie film Bound, tried to sell him the story about a universe where men with black raincoats could jump in the air and time would freeze while everyone got a complete 360 view of their jump. Glad he turned it down.