Sport says frustration in negotiations for Inter Milan star Wesley Sneijder and Chelsea's pursuit of Tottenham's Luka Modric has led Ferguson to consider Schweinsteiger as his prime midfield signing for the summer.
The Germany international has been a long-term target for Ferguson and has admitted an ambition in the past to play for United.
A genuine midfield general, Schweini refused to shut the door on leaving Bayern last month, despite the claims of new coach Jupp Heynckes.
AC Milan have also expressed interest in the midfielder in recent weeks.
Ferguson sees Schweinsteiger as the leader his midfield needs following the retirement of Paul Scholes.