The player's agent admits the Belgian could be tempted by a move to Italy, having experienced a difficult three years at Old Trafford.
Having scored the opener during United's 2-1 semi-final win over former employers Everton on Saturday, Fellaini was spotted taking in Roma's contest with Napoli at the Stadio Olimpico just two days later, sparking fervent speculation about his future at Old Trafford.
According to Gazzetta dello Sport, the 28-year-old could subsequently be in line to complete a move to the Italian capital.
It would mark the end of what has been a difficult episode in Fellaini's career, with the midfielder largely unable to recapture the form that convinced then United boss David Moyes to spend £27 million in order to bring him to the club from Everton in 2013.
As a result, a regular place in the Red Devils line-up has proved elusive recently, and the player's agent, Luciano D’Onofrio, has suggested that a move to Italy could prove tempting, although he insists there is nothing imminent.
He told TuttoMercato: "He was probably there [at Roma] on holiday.
"For the moment I have no other news. So far I’ve had no contact with Roma for him.
"Would that move be acceptable? Yes, Roma is a possibility to consider."
Nevertheless, the prospect of selling Fellaini has excited a number of United fans, many of whom have been unimpressed by his time at the club.
He did well against Everton but Fellaini to Roma is the best Rumour I have ever heard lately better than José or Sanches— _Vignesh_ (@_Vignesh07_) April 26, 2016
Fellaini pictured in Italy for Roma v Napoli. Let's hope they make us an offer we can't refuse. A bag of crisps should do it #MUFC— The United Stand (@UnitedStandMUFC) April 26, 2016
Dear Roma, please sign Fellaini. Sincerely, every Man United fan— UnitedRed (@TheMourinho_Way) April 26, 2016
Fellaini linked with Roma. Would be good for all parties— Hamza (@DavidGillWho) April 26, 2016