The Premier League giants are in advanced negotiations with Atalanta to get a deal over the line to sign the 20-year-old striker.
They have already agreed personal terms on a contract with Hojlund and he has prioritised joining Manchester United despite interest from Paris Saint-Germain.
The talks between the two clubs have entered a decisive phase and there is a will to get a deal over the line soon.
According to Sportitalia, Manchester United are trying to reach a broad agreement with the Italian club by the end of today.
Hojlund is already in England where Atalanta are set to play Bournemouth in a pre-season friendly.
If an agreement is close to being agreed upon, the forward might not feature in the game.
Manchester United have improved their offer to €62m plus another €5m in performance based add-ons.
Atalanta want somewhere around €68m to €70m and the final package to touch the €75m package.
