Spurs could be after a striker with Vincent Janssen and Fernando Llorente's future in doubt.
The 23-year-old has been forced to watch a lot of football from Hertha's bench this season, making 10 consecutive Bundesliga substitute appearances before being handed his first league start of the season on December 1.
The Germany Under-21 international's form has been affected, scoring only one goal in 15 top-tier German league games - a stark contrast to least season's excellent form.
Selke scored 14 goals in 31 league and cup appearances - as well as adding four assists. It is not only his goalscoring form that has caught the eye of Premier League clubs in recent times, but it his contribution and work rate too.
The report claims Mauricio Pochettino is very fond of Selke, who has also played for RB Leipzig an Werder Bremen after coming through the ranks at Hoffenheim. The 6ft 4in striker has a contract at Hertha until the summer of 2022.
Renowned for his prowess in the air and offering somewhat of a plan B, Selke is said to be "ready to talk" to Tottenham should they come calling. The new Stadium is also said to be tantalising to the striker.
But Spurs face competition from ex-RB Leipzig manager Ralph Hasenhüttl, who is keen to bring the striker to Southampton and will know him well - after selling Selke to Hertha in the summer of 2017.
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