The 33-year-old is a free agent having left PSG at the end of last season and he is expected to fly into Manchester on Sunday ahead of completing a move before Monday’s transfer deadline.
It is understood that a deal would be for a year with the option for a further 12 months, with the move for Cavani giving Ole Gunnar Solskjaer an alternative option up front.
Odion Ighalo, who has been acting as back-up since January, will head back to Shanghai Shenhua in the new year, with the Nigerian having struggled for form and regular minutes since the restart.
Solskjaer has tried to move away from signing senior players and has focused on bringing young, British talent to the club since he took over as manager when Jose Mourinho was sacked.
While Cavani goes against that trend, it is understood the club believe bringing in a proven winner can help to further the development of the younger players.
The deal for Cavani is not expected to have any impact on the last-minute transfer business United are trying to complete ahead of Monday evening’s deadline.
Jadon Sancho is still a priority target despite Borussia Dortmund being adamant that the winger is not going anywhere - sporting director Michael Zorc again reiterated on Saturday that United had missed their chance to sign the Englishman.
The club are also working on alternative options should a deal for Sancho not be able to be finalised, with Barcelona winger Ousmane Dembele one of the names on the Plan B list.
There has, however, not been a formal bid put to the Catalan giants and United would only be interested in bringing the 23-year-old in on a season-long loan deal, should the move for Sancho collapse.
In terms of outgoings, discussions are continuing with Roma over a permanent deal for Chris Smalling, who impressed during his loan spell at the Italian side last season.