UPDATE 1-Soccer-Liverpool teenager Duncan joins Fiorentina

* Duncan moves for reported 2 mln euros

* Deal contains 20% sell-on clause

* Winger Kent joins Rangers (Adds Ryan Kent moving to Rangers)

Sept 2 (Reuters) - Liverpool striker Bobby Duncan has moved to Fiorentina in a permanent transfer on the final day of the European window, the Premier League club said on Monday.

Financial details of the deal were not disclosed but local media reported that the Serie A club would pay European champions Liverpool about two million euros ($2.23 million) for the 18-year-old and that the contract included a 20% sell-on clause.

"Bobby Duncan has today completed a permanent transfer to Serie A side Fiorentina," Liverpool said on their website https://www.liverpoolfc.com/news/first-team/363383-bobby-duncan-completes-move-to-fiorentina.

"The 18-year-old striker makes the move to Italy after one season with Liverpool, during which he scored 32 goals at Academy level.

"Everybody at the club wishes Bobby the best of luck in his future career."

The move follows criticism of Liverpool by the player's agent Saif Rubie, who alleged on social media last month that the Anfield club were holding his client against his will after they rejected a loan offer from the Italian side.

In response to Rubie's comments, Liverpool said: "Liverpool Football Club is aware of and disappointed by the unattributed comments and unfounded allegations that have been made in the media regarding one of our players.

"We will, however, continue our efforts to work privately with the player to find resolution in the best interests of all involved."

Liverpool winger Ryan Kent also left the club before the window closed, sealing a permanent move to Scottish side Rangers, with whom he spent last season on loan.

Rangers said that Kent had signed a four-year deal and British media reported that the club, who are managed by former Liverpool midfielder Steven Gerrard, paid seven million pounds ($8.59 million) for him.

"Rangers are delighted to confirm the return of Ryan Kent," the club said on its website https://rangers.co.uk/news/headlines/gers-sign-ryan-kent. "The 22-year-old will join up with Steven Gerrard's squad when the team return from the international break."

($1 = 0.8973 euros)

($1 = 0.8145 pounds) (Reporting by Simon Jennings in Bengaluru; Editing by Ken Ferris / Ian Ransom)