Pogba suffered a thigh injury while on international duty with France in November.
The club responded by sending the 28-year-old to a warm-weather training camp in Dubai to aid his recovery, with the midfielder expected to be available again in the New Year.
The decision to send Pogba to the United Arab Emirates was sanctioned before Rangnick’s arrival at Old Trafford, when Ole Gunnar Solskjaer was in charge.
And the interim boss has questioned the logic behind the move, insisting players who pick up long-term injuries in the future will undergo their rehabilitation in Manchester.
‘My former clubs were always trying to make sure the rehab should take place in the club itself,’ Rangnick said.
‘As far as I can tell, the medical department is really good, very good, with many different approaches towards rehab.
‘I would not want players to do their rehab abroad or anywhere else but the decision on Paul was taken before I came.
‘In the future, I have already spoken to the medical department – to Steve [McNally] our doctor, to (head of physiotherapy) Robin Sadler – that in the future I want players with injuries – and hopefully we don’t get long-term injuries – but if we have them in the future I want them to stay here.’
Pogba is in the final year of his contract at United with Rangnick insisting he will not try convince the France international to extend his deal if he has already decided to move on.
MORE : Ralf Rangnick insists he will not try to convince Paul Pogba to sign new Manchester United contract
MORE : Barcelona plot move for former Manchester United starlet Adnan Januzaj
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