The Napoli frontman is in demand with less than a fortnight of the transfer window remaining.
Spurs boss Jose Mourinho wants Milik to bolster his attacking options, but largely as back-up to Harry Kane.
A deal between Spurs and Napoli looked to be heading in the right direction but Mourinho is said to be haggling over the terms of a deal.
That has opened the door to other clubs, with United among several sides to have held discussions regarding the Polish international, according to Rai Sports’ journalist Ciro Venerato.
“The latter are the most reliable track, but the formula requested by Napoli does not convince Mourinho.”
Milik looked to be on his way to Roma earlier this summer, but that switch was scuppered when Edin Dzeko’s proposed transfer to Juventus collapsed.
Manchester United are looking to plot their path back to the top. Ole Gunnar Solskjaer has already brought in Donny van de Beek but Jadon Sancho remains Manchester United’s number one target.
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United are in the market for reinforcements before the window slams shut, though a forward is not considered as a priority.
Porto’s Alex Telles looks like he could be the next name through the door at Old Trafford as United chiefs continue to work on an £17million deal for the left-back.
Meanwhile United are also hopeful of prising N’golo Kante from rivals Chelsea in a £60m deal.
Mirror Football revealed United had made enquiries regarding the Frenchman with Chelsea seemingly prepared to let him leave the club for the right offer.
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United have turned their attentions to other targets after failing to land Jadon Sancho, though central midfield is an area of the pitch where the Red Devils are pretty well stocked.
Meanwhile United are still working to move on Chris Smalling with the defender keen to return to Italy.
Roma want to re-sign the 30-year-old permanently but Inter Milan could swoop in to land his signature.
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