With Reds boss Roy Hodgson keen to strengthen his attacking options in the January window, Pogrebnyak would prove to be a key signing with injuries to Fernando Torres and Dirk Kuyt exposing a threadbare front-line in the past month.
Hodgson has reportedly been promised £30million from new owners NESV to spend in 2011 and the striker would command a fee in the region of £12million.
A move to Spurs, meanwhile, would see Pogrebnyak link up with his Russian team-mate Roman Pavlyuchenko.
Bobic told Bild newspaper: "I have been listening to rumours that Liverpool and Tottenham have their eyes on Pavel.
"It's a fact. However, none of these clubs have been talking to us about him lately. He is a player of VfB Stuttgart."