The France international playmaker is a major target for the Gunners.
Arsene Wenger has targeted the Lyon star as he looks for a successor to Alexis Sanchez.
Fekir could replace Sanchez in Arsenal’s attack with the Chilean set to leave for Manchester City at the end of the campaign when his contract expires.
But while Arsenal have looked to seal the 24-year-old’s arrival in time for the New Year, they have hit stumbling blocks.
Lyon president Jean Michel-Aulas insisted last month Fekir would not leave in January.
The player himself, though, recently raised doubt over his future in Ligue 1 by admitting this could be his last season at Lyon.
He revealed Arsenal, Manchester United and Manchester City are among the clubs he would consider leaving for.
However, despite Fekir’s contract being due to expire in 2020, Lyon are holding firm.
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Starsport understands the French club are still refusing to sell to Arsenal in the New Year.
Fekir won’t leave for the Emirates in the January transfer window with Lyon still fighting on domestic and European fronts.
They still have outside hopes of winning the Ligue 1 title, with leaders PSG nine points ahead.
And Lyon have made it through to the knockout stages of the Europa League, where they could yet face Arsenal later in the competition.
Wenger poached Alexandre Lacazette from Lyon for a club-record fee of £52m.
Starsport understands a deal for Fekir would cost Arsenal more than that at around £60m.
While Fekir could well replace Sanchez next summer, the Gunners are still trying to convince Mesut Ozil to sign a new contract.
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Additions to the squad could still be made in January as well.
Germany forward Julian Draxler has been linked over a loan from PSG ahead of the World Cup.