New Sampdoria president Massimo Ferrero has revealed that Esteban Cambiasso rejected the chance to join the club.
World Cup revelation James Rodriguez admits it would be a dream come true to one day represent Real Madrid.
The 20-year-old signed a pre-contract agreement with the Scottish champions on Wednesday and will officially join on a four-year deal when the transfer window opens on January 1.
And, having watched Celtic in Champions League action on television back in his homeland, Fridjonsson says the decision to sign for the Glasgow side was an easy one to make.
He said: "I have seen them play in the Champions League while I was in Iceland so I know of some of the boys.
"Iceland shows every game in the Premier League and the Champions League and everybody watches football there so we can see Celtic.
"When Celtic came in, there was nothing to decide.
"I was buzzing when I heard of their interest and I was just really excited."
Fridjonsson had been playing with Fram in his native Iceland and, now their season is over, he is expected to join the Hoops for training in early December.
He has told new boss Neil Lennon he will be ready to be pitched into the action when he completes his move to Celtic in the new year.
But Fridjonsson admits he faces a battle to force his way into the first team.
He said: "I will get to know the boys better and train with them and see how it works.
"I think I can be ready. I just have to work hard.
"I'm not going to walk into the team, that's for sure."
Asked what Celtic fans can expect to see from him, he added: "I will try to score goals and hopefully I can do that for the Celtic fans.
"This is just the biggest step-up and I'm delighted.
"The physical side will be more here so I just need to get in the team and hopefully I can adapt pretty well.
"I can play up alone, I can hold up the ball well and link players to the game.
"I've got good technique, I'm good in the air and I've got a good left foot."
He believes the opportunity to play at Celtic Park and train at the club's Lennoxtown base will only make him a better player - along with the help of new boss Lennon.
He said: "The facilities here are excellent. I'm used to Iceland and it's just a hobby there almost.
"Everything is much better here. With these facilities, you can just get much better if you train there every day.
"I spoke to the manager yesterday and got good feedback from him. I think he can help me a lot."