The Spanish giants still hold the rights to 50 per cent of Garay's sell-on fee after the Argentinian defender joined Benfica from the Bernabeu.
And Benfica are keen to renew his contract, upping his release clause from €20m - but for that to happen Real Madrid have to waive their stake in the defender.
Add to the fact that Chelsea and Monaco target Fabio Coentrao favours a return to Benfica, and Real Madrid hold a clear advantage over the Stamford Bridge club in the race for Matic.
Benfica's interest in Coentrao, coupled with their desire to purchase the full rights to Garay, puts Real Madrid in a strong negotiating position for the €40m-rated Matic.
The former-Chelsea youngster has blossomed at the Stadium of Light. And reports last month claimed Jose Mourinho had identified the 25-year-old Serbian international as the perfect replacement for John Obi Mikel.
But the midfielder, who has a €40m release clause in his Benfica contract, could be let go if the Portuguese club receive Coentrao and Garay in return.
Chelsea wouldn't be able to match such an offer, putting Real Madrid ahead in the race to sign Matic. Coentrao has informed Madrid of his desire to leave the club, having struggled to dislodge Marcelo from the starting lineup.
Chelsea and Monaco have been linked, but the 25-year-old favours a return to Benfica to play under head coach Jorge Jesus - the man who got the best out of him during his first spell at the club.