Argentina international Rojo, who had undergone surgery after dislocating a shoulder in training in December, faces a race against time to get fit for United's FA Cup final against Crystal Palace at Wembley on Saturday.
United are sixth in the Premier League table and would move above Southampton into fifth with a draw or victory in their last match against Bournemouth on Tuesday.
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(Reporting by Ian Rodricks in Bengaluru; editing by Sudipto Ganguly)
