Ajax academy product Rensch arrived in Rome on Wednesday to complete his medical exam ahead of his move to the club managed by Claudio Ranieri.
Farioli left the right-back out of the starting lineup in Sunday's game against sc Heerenveen and had to leave Rensch's name out of the 23-man squad for Thursday's Europa League game against Latvian champions RFS.
"We have already said goodbye to Devyne (Rensch)", Farioli said at the press conference before in Riga.
"Personally, it was quite emotional. He's a great player and a good guy.
"He is still an Ajax player, but he is in Rome to finalize the deal."
New talent arising
With 19-year-old Gerald Alders in the squad, Farioli seems to have put another youth academy product forward to potentially fill Rensch's spot - one which was taken by Danish full-back Anton Gaaei in recent times.
"In this moment, there's a clear need. But while we are waiting, Gerald (Alders) will be with us.
"He's an important player from Jong Ajax. He's really motivated and really energetic, so we fully trust him.
"He's very energtic, really clever, a fast learner. I think this is already very good to start with.
"He's very skillful on the ball and of course with being so young and with the experience with the senior team, he will have to learn and experience it a little bit.
No truth to Roma links
Besides Rensch, Farioli himself has been the subject of AS Roma rumours. The team from the Italian capital are looking for a successor to interim boss Claudio Ranieri and the Italian newspaper Gazzetta dello Sport reported that Roma have set their sights on the Italian Ajax boss.
The 35-year-old Italian declined to answer any questions regarding a move back to Italy: "For me, there is nothing.
"I think you're starting to know me quite well about the fact what gossip and rumours are. Talks are talks.
"I have already proved myself quite well with my dedicatin to the club and now are in a moment in the market where it is quite easy to make an association and a discussion.
"Let everything outside. The reality is that there's nothing bigger than Ajax."