Fasan was associated with Udinese Calcio, before he joined Scottish Premiership club Celtic in 2010, initially on a trial basis. He kept a clean sheet in the 2011 final of the Glasgow Cup as Celtic's under-17s beat Old Firm rivals Rangers 1–0. He was an unused substitute in the 2012 Scottish Youth Cup Final, as Celtic recorded an 8–0 victory over Queen of the South at Hampden Park. He played in goal for the 2012–13 Scottish Youth Cup final, as Celtic beat Dunfermline Athletic 3–1. He turned professional at the club in August 2014 when he signed a three-year contract after impressing manager Ronny Deila during pre-season. However, he failed to establish himself as the club's second choice goalkeeper ahead of Łukasz Załuska, Logan Bailly, or Dorus de Vries. On 31 January 2017, he joined EFL League One side Port Vale on loan until the end of the 2016–17 season. He was signed by manager Michael Brown following the sale of Jak Alnwick to Rangers, leaving Fasan to compete with fellow youngsters Ryan Boot and Harry Pickering for a first team place. He made his senior debut in 3–0 defeat to Peterborough United at Vale Park on 4 February, and was named as the home team's man-of-the-match after he saved a penalty in the first-half. He also saved a penalty in his third game for the club, during a 2–0 defeat to Millwall at The Den on 11 February; Brown said that "they were fantastic penalty saves but his game has to improve". He lost his first team place to new signing Deniz Mehmet in mid-March, but returned to the starting eleven for the final two games of the season.
Bury
On 10 August 2017, Fasan signed for League One club Bury on non-contract terms. Manager Lee Clark signed him to provide cover for Joe Murphy whilst the "Shakers" boss attempted to sign Freddie Woodman. Fasan did not make any first-team appearances in this time.
Kilmarnock
Fasan signed a short-term contract with Scottish Premiership club Kilmarnock on 1 February 2018, becoming manager Steve Clarke's second goalkeeper signing inside 24 hours following the arrival of Jasko Keranovic. He featured in four games for "Killie" in the latter half of the 2017–18 campaign. Fasan was released by Kilmarnock in May 2018, at the end of his contract.
Falkirk
On 11 June 2018, Fasan signed a one-year contract with Scottish Championship side Falkirk; manager Paul Hartley said that "I am sure he will continue to progress and develop with regular game time in the coming year, we now have three very good goalkeepers on our books ". However the "Bairns" registered only one victory in Fasan's first ten games for the club and he was sent off against Morton after fouling Michael Tidser. Fasan quickly fell out the picture due to a number of poor displays and was replaced instead by two other goalkeepers in turn, David Mitchell initially and then Wolves loanee Harry Burgoyne. Falkirk went on to be relegated into League One and Fasan was released in the summer.
Sicula Leonzio
On 24 January 2020, he returned to Italy to sign with Serie C club Sicula Leonzio.
