I think so too, because Roma's performance and Roma's achievements have improved quite a bit under De Rossi. This was not very easy as he was trusted to replace Mou at Roma at that time, but slowly, he began to be able to integrate with the group more solidly.
Roma will not complete this season with a high rank enough to participate in Champions League next season. It is a task that was not achieved by Mourinho with his two completed seasons in Rome but De Rossi will not achieve anything better than Mourinho.
If simply look at result, De Rossi did worse than Mourinho, no Europa League final match (worse) and no Champions League spot (the same).
When asked by journalists, he always answered that he had not thought about discussing his contract, because they are very busy now and they will continue to focus on performance this season. But, for the signal ad what happen to Roma, I'm not sure that Roma will let de Rossi go and take riskier decision of new other coach, expect they find the very appropriate and professional coach then. But, there is indeed a signal that he will continue in Rome if you look at and understand at a glance his statement.
With finance of Roma and with acceptable performances of Roma with De Rossi, Roma will be smart enough to convince De Rossi to sign a new and longer contract with them. Because if they look for another coach, requirement in salary will be more serious than what De Rossi wants.
A next season will be important for De Rossi to prove his ability but this summer will be challenging for him and Roma. Will Lukaku and Dybala stay with them or leave?
They are very important attacking players in Roma and without either Lukaku or Dybala, Roma will have big problems in attacking. Baldanzi was bought as Roma's preparation to separate with Dybala but this young player did not play too well so far.