Discussions between the two clubs have been ongoing through intermediaries, resulting in a verbal agreement. The proposed deal is for a season-long loan with an option to purchase Rashford.
Barcelona have explored other options, including Athletic Bilbao's Nico Williams and Liverpool's Luis Diaz, but could not reach an agreement with either player.
Rashford's transfer listing at the end of last season led to interest from several clubs, with Barcelona emerging as the leading contender.