Reports this morning claimed that Roma have offered De Rossi £5m per year to stay at the Stadio Olimpico following speculation that Manchester City were monitoring the situation.
"We all know what Roma means for the Romans and that is why I am not worried," said Enrique. "He will stay because this is what he wants. At least, that's what I think.
"Someone of De Rossi's level should've renewed some time ago, but every day he trains with a smile on his face. Losing him in January is not an option.
"There are many players who don't just think about money, but also where they are happy and can do their best work."
De Rossi has spent his entire career with Roma.