The former Arsenal custodian made the suggestion following the Premier League game between the Swans and Tottenham at the Liberty Stadium on Sunday afternoon.
The match ended in a 2-2 draw, with Denmark international Eriksen scoring twice for Spurs, both from free kicks.
Fabianski has admitted that he could not do much to stop the former Ajax star’s efforts on Sunday and has suggested that he is the best free-kick taker in the Premier League.
"Is he the best? I don't know,” the Poland international told The Mirror. “I will just say he is the first player to score two free kicks against me! So that might answer the question.
"He not only gets the ball over the wall, puts a load of pressure into the shot as well. I analysed him before the game.
"I watched his free kick against Man City when he hit the bar and Harry Kane scored from the rebound. I knew what to expect but I still lost the ball.”
Eriksen is indeed superb from free kicks and is arguably the best in the Premier League for that.
Nobody has scored more direct Premier League free-kick goals than the 23-year-old since his debut in September 2013.
The former Ajax is one of the most creative players in English football and arguably the most talented outfield player in the current Tottenham squad.
In five Premier League appearances so far this campaign, Eriksen has scored two goals and created 11 chances.
Last season the Dane scored 10 goals and created 83 chances in 38 Premier League appearances, while during the 2013-14 campaign he found the target seven times and created 68 chances in 25 league matches.