Reports on Thursday suggested the Dutchman could be one of many to be sold by the Carling Cup holders this summer as they look to freshen up their squad at the end of the season.
Kuyt has struggled to hold down a regular starting place under manager Kenny Dalglish, with summer arrival Jordan Henderson often preferred in his wide right position.
The 31-year-old conceded last month he may be forced to leave the club if he continues to find first-team opportunities limited.
And the player’s agent, Rob Jansen, insists the former Feyenoord ace is keeping his options open, with a possible move to Roma an attractive proposition for the player.
"(Dirk) Kuyt is considering his future," Jansen told pagineromaniste.com.
"He still has a contract with Liverpool which expires in 2014.
"AS Roma could be an option for Dirk. They are a prestigious club that is fighting for important objectives. With (Roma's sporting director, Walter) Sabatini there is an excellent relationship.
"I can say that Roma is part of the list of clubs that Kuyt would take seriously into account."
The Dutchman was imperative in the Reds Carling Cup win over Championship outfit Cardiff City, netting in extra-time and scoring a penalty in the resulting shoot-out.
