Portugese newspaper A Bola claims Mourinho has persuaded the Chelsea owner to free up funds for a €40m offer for the former-Stamford Bridge youngster.
Abramovich's reluctance stemmed from the fact the Blues had let Matic leave the club for free as part of the deal that brought David Luiz to Stamford Bridge.
Luiz was signed for €25m, with the €5m-rated Matic included as an added extra.
But the Serbian international has become one of the most impressive players in the Liga Sagres, and Mourinho is keen to recruit him this summer.
The 24-year-old has a €50m release clause in his Benfica contract, but A Bola claims talks between the two clubs are at an advanced stage and Chelsea are willing to meet Benfica chairman Luis Filipe Vieira's €40m valuation of the player.
Earlier this week Matic revealed he'd enjoy another campaign with the Portuguese runners-up, but admitted he's flattered a manager like Mourinho is a fan.
He insists he's focussed on improving his game with Benfica for at least another season, and wants the opportunity to play in the Champions League final with Benfica at the Stadium of Light - the Portuguese club's home ground hosts next year's showpiece.
Still, the latest report from Portugal claims Mourinho will test Matic's commitment by offering him a route back to Chelsea, and the opportunity to prove himself in the Premier League, and to those that let him go in the first place two years ago.
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