ESPN says the Uruguay striker has had a change of heart and will announce his decision next week.
Cavani was understood to be concerned about his lack of playing time at United and was also angry over his treatment at the hands of the FA who hit him with a three-match ban and £100,000 fine for using the word 'negrito' in a social media post.
Last month his father Luis said: "My son does not feel comfortable in England and wants to be close to the family again. Edinson is going to end up playing in South America – he would like to play for Boca."
But it now appears that the former Paris Saint-Germain and Napoli striker is ready to extend his career in Europe by another season and stay at United.