Reports in Spain suggest Gunners chiefs are plotting a surprise move for ex-Tottenham midfielder Modric.
According to Don Balon, Arsenal are ready to offer Real Madrid £53million for the 32-year-old.
And Ladbrokes have reacted to the speculation by offering odds of 2/1 that Modric returns to north London in a red shirt.
“It would go down as one of the most shocking transfers of recent windows if Modric opts to join Arsenal, but the odds suggest there’s every chance of a deal happening,” Ladbrokes spokesman Alex Apati said.
Modric spent four seasons at Tottenham after joining from Croatian outfit Dinamo Zagreb in 2008.
He established himself as one of Europe’s leading midfielders during his stint with Spurs and was snapped up by Real Madrid for around £30m.
Modric has proved to be a bargain buy for the Spanish giants, helping them to three Champions League titles and La Liga glory last year.
But the 103-cap Croatia international could find himself a victim of a squad refresh at the end of the season.
Modric has also been linked with a return to Tottenham and Ladbrokes price that potential move at 3/1.
He could, however, swerve a move back to England and try his luck in Serie A.
AC Milan are 9/2 to win the race for his signature while a move to Juventus is available at 5/1.
Modric has previously suggested that he would like to retire at Real Madrid.
“Signing for Real Madrid was a dream come true,” he said in December.
“There aren’t that many players who have managed to retire here but we’ll see what happens with me.
“My wish is to retire here but things change very quickly in football.”