The Croatia international, who departed the north London club in 2012, is out of contract in the Spanish capital at the end of the season.
Modric is therefore free to begin negotiations with other clubs over a pre-contract agreement from 1 January.
According to a report in El Chiringuito de Jugones (via Marca), Mourinho has contacted the 35-year-old to try and convince him to return to Spurs.
The Portuguese boss was in charge at the Bernabeu when Modric moved there eight years ago.
He has already overseen the capture of two Real Madrid players during his time as Tottenham manager, signing Sergio Reguilon and Gareth Bale over the summer.
However, Madrid head coach Zinedine Zidane is understood to want Modric to sign fresh terms.
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