It is claimed Rashford will travel to America where he will be put through his paces during a working holiday next month.
He is then expected to return for the start of pre-season with United on June 27.
Rashford is also in a fight for his international place, having been left out of the England squad for the March internationals.
He was again omitted by Gareth Southgate on Tuesday for England’s four upcoming Nations Cup matches next month.
Rashford is at risk of losing out on England’s squad for the 2022 winter World Cup in Qatar.
His last cap came in July 2021 during the finals of the Euros, where he agonisingly missed a spot kick in the penalty shootout.