The Manchester United defender spent last season on loan at the Serie A club, and has been in negotiations over a potential return all summer.
But - in something of a theme of this window - the Old Trafford hierarchy want a permanent deal.
Roma are unwilling to move for that, and have been offered the option of taking back Rudiger instead.
The German centre-half has been frozen out at Chelsea.
Tottenham still retain hope of signing him, and feel Jose Mourinho can persuade the player to stay in London.
Wages would not be an issue, and the club could arrange a loan with option for a permanent deal.
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