United manager Jose Mourinho is seeking a new centre-back and 25-year-old De Vrij is available for £30million.
But Italian newspaper Gazzetta dello Sport claim an agreement between Inter and De Vrij has already been struck – and that the scouting mission is merely a formality to reassure Inter they have the right man.
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According to the report, scouts will be at Holland's clash with Bulgaria in Sofia tomorrow night, before attending Tuesday's friendly between Italy and the Dutch in Amsterdam.
It is claimed Inter have a four-year deal for De Vrij ready for the ex-Feyenoord star to sign.
The relationship between the player and his current club has broken down after Lazio tried to get De Vrij to sign a new contract – only for him to reject the terms.
Inter Milan are ahead of Man United in the chase for Stefan de Vrij
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De Vrij's Lazio contract expires in 2018
Inter scouts will watch De Vrij (right) in action for the Netherlands tomorrow
Lazio risk losing De Vrij on a free transfer when his contract expires in 2018, meaning they will likely sell up in the summer.
As for United, they may be behind Inter in the race to sign De Vrij but their extensive scouting network means they have other targets.
Mourinho brought in Eric Bailly last summer but appears keen to strengthen further, with the futures of Chris Smalling, Phil Jones and Matteo Darmian all in doubt.