Cavani, 33, remains a free agent after a summer full of speculation about his future.
The Uruguayan marksman was close to Benfica, but the Portuguese side could not agree personal terms and called off talks.
Atletico Madrid also like Cavani, but any move for him would depend on Diego Costa leaving – which is looking less likely at this stage of the transfer window.
United are in contact with Cavani’s brother and agent Walter to discuss personal terms over a potential deal.
Cavani is reportedly the preferred option for United’s owners, but his salary demands are an obstacle.
Jovic the alternative
The other candidate for the Red Devils is Real Madrid forward Jovic, who would arrive on loan.
Jovic, a €60m signing from Eintracht Frankfurt last summer, had a disastrous debut season in Madrid.
Zinedine Zidane has given him a start in Madrid’s 3-2 win over Betis at the weekend, but he again failed to impress.
However, the Serbian remains highly rated on the continent and a number of clubs have expressed an interest.
Jovic would cost less than Cavani and is younger, making him an appealing option for United chiefs.
Madrid and Jovic agree that he should join the club that will guarantee the most playing time.