The 31-year-old, who has one year left on his existing deal at Liverpool, is set for the exit as manager Kenny Dalglish looks to lower the average age of his squad.
And Rob Jansen, Kuyt’s agent, says the Dutch international would welcome a move to the Italian capital.
Speaking to Pagine Romaniste, Jansen said: "Kuyt is considering his future. He still has a contract with Liverpool, expires in 2014. Roma could be an option for Dirk. It's a prestigious club that is fighting for important objectives. For now I can say that Roma is part of the list of clubs that Kuyt would take seriously."
Kuyt, a virtual ever-present since signing from Feyenoord in 2006, has seen his first-team opportunities reduced this season - he has made just 19 Premier League starts - and last month hinted that he would consider his future after being left out of the starting line-up for February’s Carling Cup final.
European giants Galatasaray and Fiorentina have also indicated their interest in signing the Dutch international, as have former club Feyenoord.
However, Jansen does not feel Kuyt is looking for a move back to his homeland at this stage in his career.
"Feyenoord know that Dirk will join them once he returns to Netherlands," he added. "But when? It’s impossible to answer that question."