The vice president of Boca Juniors, Juan Roman Riquelme, is personally handling the negotiations with the Uruguay forward, the source said.
Cavani has scored seven goals in 27 games since moving to Old Trafford on a free transfer in October. He signed a two-year contract, but both the 34-year-old and United have the option to cut short the deal in the summer.
United and Cavani also have an option to add an additional year in the deal signed last October. If United decided to not execute the option, the club will have to pay him a €2 million release clause.
"He has the option to continue in Manchester, where he feels very welcome, but the option to return to South America at this point is very real," one of the sources said. Those close to him think that "he ultimately will be the one making the decision" and that "it seems he has it [decision] all very clear."
Sources told ESPN last week that United are keen to wait until Cavani has recovered from injury before making a decision about his future.
Sources earlier told ESPN that Cavani's plan is to stay in Europe next season to compete in the top leagues ahead of the 2022 World Cup in Qatar.
Luis Cavani, the father of the Uruguay striker, told Argentina's TyC Sports last month that his son had a "60% chance of joining a South American club" and would be inclined to play for Boca Juniors.
After his father's interview, Cavani posted a picture on Instagram of him celebrating a goal for United alongside a message in Spanish saying that he is "proud" to wear those colours.
Cavani, 34, was upset after he was sanctioned by the FA with a three-game suspension earlier this season for using a racial term in a social media post since he considered the expression in Spanish -- negrito -- to be a word used in an affectionate way in his country.