The Red Devils boss has so far strengthened his squad with the addition of three new faces, bringing in Victor Lindelof, Romelu Lukaku and Nemanja Matic for a combined £146m ahead of the 2017-18 campaign.
Mourinho has yet to finish his summer spending, according to the Daily Record, as he plans on going all out to sign unsettled Tottenham defender Rose in the remaining weeks of the window.
Rose's public comments that he would consider leaving Spurs if an offer is tabled is said to have piqued the Portuguese's interest, with rotation expected to be a regular occurrence at full-back this coming season.
The same report suggests that Chelsea have already made an approach, however, potentially kickstarting a bidding war for the England international.
A Leeds United academy product, Rose has spent the past decade in North London and remains under contract until 2021.