Klose, 32, is available on a free as his contract at Bayern Munich expires this summer. The Germany international has scored just one goal in nine league appearances this season for Bayern, losing his place in the side behind Mario Gomez and Thomas Muller.
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Spurs are known to be in the market for a striker, with Robbie Keane expected to leave in the Summer, and rumours linking Roman Pavlyuchenko with a White Hart Lane exit. In January Tottenham reportedly had bids for Guisseppe Rossi, Fernando Llorente, and Diego Forlan rejected.
Klose has proved himself to be one of the best strikers in world football in recent years, scoring 14 goals in World Cup finals which puts him just behind all-time record scorer Ronaldo.