Fekir's form this season has drawn interest from a number of Europe's biggest clubs, with the 24-year-old having scored 21 goals in just 33 appearances across all competitions.
Fekir's agent recently suggested that his client could leave Lyon at the end of the season, leading to increased speculation over where his next destination could be.
However, Spanish publication Sport reports that Barcelona have now withdrawn their interest as they already have too many players in his position and are also looking to sign Arthur.
The news will come as a boost to Arsenal, who are understood to have made Fekir their main transfer target this summer.
The report also claims that Barcelona have turned down a move for Fekir's 19-year-old Lyon teammate Houssem Aouar as well.