Manchester United boss Louis van Gaal has told chief executive Ed Woodward to get busy.
Muller, 24, has felt marginalised by new manager Pep Guardiola and is seeking reassurances from Bayern that he remains a key player, while Schweinsteiger, 29, is open to the idea of joining United.
Both played under Van Gaal at Bayern in the team that won the double and reached the Champions League final in 2010.
The pair have enormous respect for the Dutch coach and would be happy to move to United if they feel their careers are stalling under Guardiola.
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