The Mirror says they signed the Uruguayan striker, who was a free agent, to a one-year deal earlier this month.
United do, however, have the option to extend the 33-year-old's current deal by a further 12 months.
The Old Trafford brass could be tempted to do just that as it's claimed he's "made a very good impression" on everyone at the club in his first week of training at Carrington.
He will, however, have to produce results on the pitch to be rewarded with a 12-month extension.
Cavani and his Manchester United team-mates will be back in action on Wednesday night, welcoming RB Leipzig to Old Trafford for their second Champions League Group H match.