The Daily Star says Germany international Schweinsteiger has endured a difficult season at Bayern Munich, having often been booed off the pitch.
And he is thought be looking for an exit route - with Tottenham hot on his heals.
Schweinsteiger said: "When things were not going well, we were being whistled at immediately in the Allianz Arena, but that sort of thing does not happen in England."
Spurs boss Harry Redknapp is on the hunt for new signings ahead of next season's Champions League play-offs.
And Schweinsteiger would be the ideal high-profile signing to kick off their campaign.