The former Barcelona B coach admitted that the former Italy international cannot play forever and also received the support of director general Franco Baldini
The 41-year-old acknowledged the vital role that his captain plays at the club and declared his wish that he could continue to represent his side.
"[Totti] is the most important player for what he represents but unfortunately he's 35 and won't play until he's 50. If only it were that way," Luis Enrique stated in a press conference.
"The team must not think that it is all over without Totti, because the future of Roma is without Francesco on the pitch."
The Spaniard has struggled to gain consistent results from his side this season yet they remain just five points adrift of third-placed Lazio and a potential spot in the Champions League
"This has for sure been a peculiar year for me and for the club. As for me, with self-criticism, that isn't to say one is 100 per cent wrong."
Roma director general Franco Baldini also attended the press conference in a show of solidarity between the club and their trainer amid reports that Luis Enrique could be on his way out at the Stadio Olimpico.
"I am here to say that the club know very well what kind of a path they have taken and the difficulties that they would face," Baldini stated.
"The quality of the players we bought is important and the quality of Luis Enrique is even more extraordinarily important.
"The club is solid, united and compact. There is unity of intent which is the guarantee of what will be an important future."