Fred will be in the north-west of England when Brazil play a friendly against Croatia at Anfield on June 3rd and the newspaper says United are keen to get a deal completed while the midfielder is in the UK.
The player yesterday spoke openly about the interest in him from Manchester rivals United and City.
Fred has been included in the Brazil squad for the tournament in Russian Federation and will be flying to England next week to play in a warm-up game against Croatia at Anfield, with United hoping to finalise their move to sign the 25-year-old when he arrives in the north west of England with his global colleagues.
Since then, the Citizens have bowed out of the pursuit of former Internacional man, and this has allowed United with a free run to pursue the midfielder's signature.
Shakhtar Donetsk president Rinat Akhmetov has confirmed negotiations took place with Manchester City over Fred in January, but the midfielder is reportedly set to sign for Manchester United. The midfielder was also a target for Spanish champions Barcelona.
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Jose Mourinho noted last month that a new contract was "very close" to being agreed with Fellaini, making it clear that he wanted to keep the player.
Yet it remains to be seen quite where he will fit in among Manchester United's star-studded squad and whether he can flourish under Mourinho at Old Trafford.
Fred has played for Brazil seven times and is set to feature for his country in Russian Federation this summer.
The Man United boss wants to bring in Fred before the World Cup, so a deal could be signed and sealed in a matter of weeks.
Mourinho had also been looking at Serbian worldwide Sergej Milinkovic-Savic, but the Italians' refusal to budge from their €100m asking price, despite missing out on the Champions League this season, has seen the Premier League side look elsewhere for midfield reinforcements.