Sarries boss Mark McCall had urged the clubs to approve Morrow’s dual role, telling the BBC he hoped all parties “can come to an arrangement that suits everybody”.
“I can understand why he is in demand because he is outstanding in his field. Hopefully small-mindedness doesn’t get in the way of a good decision,” added McCall.
However, Harlequins scrum-half Danny Care – who retired from international duty earlier in the year after winning 101 caps – has been among those to question how manageable a job-sharing position would be, considering Morrow would have access to key medical information regarding England players when on Saracens duty.
“I can understand why there will be a hesitation from other Premiership clubs,” Care told the Rugby Union Weekly podcast.
“I would say there is a conflict of interest – and I am not in any way questioning Phil Morrow’s integrity.
“I have no doubt Phil Morrow would do an unbelievable job in that role, but it doesn’t seem right to me.”
Borthwick has spent the last month rebuilding his backroom staff after the departures of Walters and fitness coach Tom Tombleson, as well as the surprise resignation of defence coach Felix Jones.
England start their new campaign against New Zealand at Twickenham on Saturday, 2 November.