I don’t think you’ll find a direct answer. But there is an indirect one. As Benedictgal posted from th GIRM, the priest is to return the place designated for the Hosts (ie the Tabernacle).
Since a layperson (man or woman) is an extra-ordinary minister of Holy Communion, that means 2 things. 1 that they can only be deputed to actually help with the distribution of Holy Communion and nothing more (beyond what the GIRM allows) and that 2 they can only do so when there’s genuine need. Since there is a priest present (at Mass, there must be), there’s no genuine need for laypersons to put the Eucharist into the tabernacle; the priest can certainly do this himself and doesn’t need any help. Since there can’t be any legitimate reason for the priest not-to-do this himeslf, laypersons can’t be deputed to do it for him.
Now, please dear readers and posters, note that I said “any legitimate reason” because no doubt, there will be those who want to come up with all kinds of wild possibilities for why the priest can’t go to the tabernacle himself.