It looks as if the club has told Mourinho that Shaw is good enough, and to get something out of him to be honest; apparently they didn’t want to sanction a move for Rose as they couldn’t see why you’d do so at the expense of one of the best young players in his position in Europe.
If this is the case, it’s clever on behalf of the board, because his second spell at Chelsea showed that talented young players that he is reluctant to work with would have been long-term assets to the club once he inevitably moves on (see De Bruyne, Salah, Lukaku, Bertrand)
Shaw can and hopefully will be United’s leftback in 5 years - Mourinho will be long gone by then.