Manchester United defender Rojo has been a first-team regular for United in Jose Mourinho's first team in charge.
The 26-year-old cost United £16million when arriving from Sporting Lisbon in 2014.
And The Sun claim a new deal is in the offing for Rojo, who has already played 35 games for United this season.
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According to the report, Mourinho plans to begin talks with the player over a contract extension.
It is claimed the manager wants to offer Rojo a further 12 months to his £100,000-a-week contract that expires in 2019.
United want to avoid a situation where the player enters the last year of his contract and potentially leaves on a free transfer.
Manchester United are set to offer Marcos Rojo a contract extension
Rojo helped Manchester United win the EFL Cup this season
Rojo (right) has played 35 games for Manchester United this season
Rojo has been one of Mourinho's most reliable players this season, having proven his worth during a defensive crisis over the Christmas period.
He was on the bench for the 3-1 win over Middlesbrough on Sunday, with Mourinho opting to play Eric Bailly, Chris Smalling and Phil Jones in the centre-back positions.