The 28-year-old has recently been linked with the likes of Manchester City and Chelsea.
The midfielder has just one year left on his current contract with Roma.
“His renewal? We hope to end before the beginning of the season,” said Roma chief executive Claudio Fenucci.
“In the next few days there will be a meeting with De Rossi’s agent to see if it is possible to take further steps forward.
“Our aim is to get an agreement as soon as possible.”
