Cavani seems set to leave Paris St Germain when his contract expires at the end of the season.
It's been widely reported that the Uruguayan has a pre-contract agreement in place with La Liga challengers Ateltico Madrid.
Cavani is believed to have agreed a two-year deal that would see him move to Madrid in June.
However, it's understood that nothing has been officially signed as of yet, so the door remains ajar for other suitors to make offers.
United are reported to have had initial discussions, but any offer may depend on the likelihood of Champions League qualification.
Ole Gunnar Solskjaer is keen to add an experienced finisher to his ranks who can add some bite to his attack.
Marcus Rashford and Anthony Martial, despite hitting some mid-season form, are yet to truly assert themselves through the middle.
Chelsea, meanwhile, have made a formal enquiry as they hunt for a proven goalscorer to compete with the impressive Tammy Abraham.
It's expected that Olivier Giroud will leave Stamford Bridge this month as he goes in search of more regular football.
Frank Lampard has frustrated both Giroud and the France national team coach Didier Deschamps with his reluctance to use the 33-year-old.
A stumbling block for both clubs is that Cavani himself seems to have his heart set on playing under Diego Simeone at Atletico.
The Argentinian coach appears to have more clout than the two ex-players just starting out their managerial careers.
Cavani is due to meet with PSG director Leonardo to discuss any possibility of leaving the club this month.
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