Croatia international Modric has been linked with a departure from the Bernabeu as part of Real Madrid’s summer revamp.
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And, according to Don Balon, the former Tottenham ace has an offer on the table from Arsenal.
But the Spanish publication claim north London rivals Spurs are in the market to re-sign Modric.
Modric has established himself as one of Europe’s leading midfielders since leaving Tottenham for Real Madrid in 2012.
He was voted the worst signing of the season during his first campaign at the club but has gone on to win three Champions League titles.
Despite being an integral part of Zinedine Zidane’s starting XI, Modric’s future has been the subject of speculation in Spain.
The 32-year-old is reportedly open to securing one last bumper contract but Cristiano Ronaldo could scupper any potential transfer.
According to Don Balon, Ronaldo believes it would be foolish for the club to sell Modric.
And the Portuguese forward has reportedly warned him against leaving.
Modric 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.”
Modric spent four seasons with Tottenham following a move from Dinamo Zagreb in 2008.
He chipped in with 17 goals and 27 assists in 160 appearances for Spurs so it would be a shock to see him sign for Arsenal this summer.
The Gunners are expected to rebuild their squad when the transfer window reopens, despite the uncertainty surrounding Arsene Wenger’s future.