Jose Mourinho is keen to land a marquee signing and the Mirror claim the Frenchman is in his sights.
The Portuguese's priority transfer target had been Atletico Madrid star Antoine Griezmann.
But with his priority now on signing a No 9 and Atletico being put on a transfer ban this summer – Mourinho has now turned his attentions to Lacazette.
Atletico had been preparing to sign the Frenchman as Griezmann’s replacement but FIFA’s punishment has thrown a spanner in the works.
Alexandre Lacazette is wanted by Manchester United and Arsenal Manchester United fans suggest Antoine Griezmann alternatives Thu, June 1, 2017
Click to reveal who Man Utd fans want to sign if a deal for Antoine Griezmann doesn't happen
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The report suggests Manchester United face competition from Arsenal though with the Gunners also in the race to sign the talented forward as Arsene Wenger looks to bring in a new forward.
Liverpool are also said to be monitoring his situation, but United would be able to outbid their rivals when it comes to meeting his wage demands.
The striker’s 37 goals this season has seen the Premier League giants show a firm interest.
Lacazette has been on Arsenal’s radar for some time with Wenger a long-term admirer of the 26-year-old.
Jose Mourinho is keen to land a marquee signing this summer
But they face a tough task in convincing him to choose the Emirates over Old Trafford after failing to secure Champions League football for next term.
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"[The team I will join] will have to be in the Champions League and play good football,” said Lacazette last month.
“Passing the ball, not just hitting it from box to box. Not kick and rush. That would not work for me,"
Lacazette has two years left on his present contract at Lyon.