The ex-Liverpool wide man has been told he can quit the German outfit this summer, after falling out with the club's coaching staff during pre-season.
The 25-year-old has been omitted from the Hoffenheim squad for their Austria training camp, and will now stay behind and train with the reserve team, as he bids to find himself a new club.
Newcastle and Swansea have already expressed an interest in singing the Dutch flyer, and now reports in Holland claim Tottenham are set to join the race.
Hoffenheim, who beat Spurs to Babel's signature in 2007, are ready to take a hefty hit on the £8million they paid Liverpool, by listening to offers of around £3million.
Babel is said to be desperate to return to the Premier League, and is willing to take a cut from his £50,000-a-week wages to seal a switch.