The Red Devils have been long-time admirers of the Galatasaray and Sporting CP strikers as they assess summer reinforcements.
According to Fabrizio Romano, United are closely monitoring both players ahead of a potential move.
He wrote in his Give Me Sport column: "There are a lot of rumours about Manchester United as they’re attentive to several situations including Osimhen and Viktor Gyokeres.
"But the budget is going to be crucial to understand what they can really do in the summer in terms of spending, investments and limitations for Financial Fair Play.
"So there is nothing concrete or advanced yet, they are just being informed on the situation with weekly updates.
"Sources close to the story guarantee that all rumours on Man United scouts traveling to follow Osimhen’s progress at Galatasaray are wide of the mark.
"As they don’t even need to 'check' on this kind of player.
"They like him, but the financial package will make the difference. The same as for Gyokeres."