Matic, a former-Chelsea midfielder, has been scouted by Old Trafford officials, and the report claims Sir Alex Ferguson has prioritised the signing of a central midfielder this summer.
The 24-year-old has been a long-term target for the United boss, and has impressed this season as an unbeaten Benfica side have stormed to the top of the Liga Sagres table.
The Serbia international didn't make the cut at Stamford Bridge, and moved to the Portuguese side as part of the deal that brought David Luiz to west London.
Benfica now value him at £45m - a fee that would make him one of the most expensive midfielders of all-time.
The Portuguese league leaders hope the mammoth asking price will put Manchester United off, and encourage them to explore alternative targets.
The 6ft 4in midfielder primarily operates in a defensive capacity, and he's got five caps for Serbia.