Roma still hasn't signed a new contract with De Rossi right? I still see it on Transfermarkt like the current contract ends up by the end of the month. Maybe it won't be that easy for him to move on with the team. I assume De Rossi wants to stay. But it is hard to predict the board for now after the team couldn't make it to the Champions League. 
I believe the board shouldn't be unfair. He didn't have much time to achieve success. Changing managers too often isn't a good way to make it. They should be patient with De Rossi and give him a chance next season as well. I think they have a good potential with him.
The information at Transfermarkt apparently hasn't updated yet because according to the that site De Rossi contract will be expired until at the end of this month but the true information is on April actually Roma has give contract extension for De Rossi for 3 years duration this because Roma owner satisfied with De Rossi performance this season in charge of Roma so Roma confirmed will not changing the manager because next season De Rossi will still at this team so if De Rossi can works until his contract duration ended then he would be at Roma until 2027 and indeed next season De Rossi will attempts to bringing Roma to finish at Champion League zone and De Rossi was confirmed this is one of his main targetI believe the board shouldn't be unfair. He didn't have much time to achieve success. Changing managers too often isn't a good way to make it. They should be patient with De Rossi and give him a chance next season as well. I think they have a good potential with him.
I can see De Rossi will attempts to make big changes in Roma and build his own squad in this team and according to his plan De Rossi this summer he will sell some players such as Leonardo Spinazzola, Rui Patricio, Chris Smalling, Rick Karsdorp, Eldor Shomurodov, Andrea Belotti, and Marash Kumbulla and the main reason why De Rossi decided to sell them because these players will not into his plan for next season besides that De Rossi also has been discuss with Roma director that he want to buy at least 3 forward players this summer and the names Alvaro Morata, Federico Chiesa and Raoul Bellanova are linked to Roma even De Rossi is very serious want to buy Alvaro Morata this because with his quality Alvaro Morata price is quite cheap and he has release clause only 15 million besides that Alvaro Morata himself has been admit that he want to leave Atletico Madrid this summer