The Netherlands international relishes forming a partnership with the Roma icon and revealed it was an easy decision to make in joining the club
Strootman, 23, recently completed his move to the Giallorossi after a €20 million switch from PSV and has been touted as a potential replacement for De Rossi, who has been linked with a move to Chelsea.
However, the Netherlands international is hoping the Italian midfielder will not exit the club as he is keen to forge a partnership with the 29-year-old.
"I have not talked to De Rossi but it will be an honour to play with him," Strootman told reporters at his official presentation. "He is a player who grew up with the club.
"We would find the best way to play together. Where I will play depends on the needs of the team. I am comfortable in any midfield role, and have played in defence and attack before.
"I'm available to the coach, I can adapt to any role."
Roma will miss out on European competition after slumping to a sixth-placed Serie A finish as well as losing the Coppa Italia final to rivals Lazio, yet Strootman remained eager to embark on his new challenge.
"Mine was an easy choice. I chose Roma because it is a great club, a world-class organisation. I spoke to [new Roma coach Rudi] Garcia and that was important to me.
"I knew we wouldn't play in Europe but Serie A has its own incentives, facing greats like Juventus, AC Milan and Inter. I know things haven't gone well here lately but I've come to Roma to win.
"[Carlos] Tevez and [Mario] Gomez, two great champions, have come as well. I'm younger than them and I want to grow to their level.
"[Maarten] Stekelenburg told me the supporters can bring a little pressure, but that means there will be more stimulus. I was greeted in an incredible way, and will give the fans my all."
Strootman joins fellow summer arrivals Mehdi Benatia, Douglas Maicon and Tin Jedvaj to reinforce Garcia's squad as they aim to get back into contention for European qualification.