The boss reiterated his interest in the wing-back as he continues pre-season training with the squad in La Manga.
Ziege, capped 58 times by Germany, only managed 11 starts in the Premiership at Anfield last season as Jamie Carragher made the left-back spot his own.
He came on as sub in the Worthington Cup Final win against Birmingham City but didn’t appear in either the FA Cup or UEFA Cup triumphs in Liverpool’s memorable treble.
Glenn revealed: “I’ve always rated Ziege and it’s been widely reported that we are interested in him but these things take time.
“There is interest from other clubs and we’re just hoping that Christian will make a decision earlier rather than later and decides to come to Tottenham.
“I feel he would be a major asset. I saw him a few years ago and I thought he was the best left wing-back in the world.
“He’ll have a burning ambition as well because things haven’t gone too well for him in the last 12 months.
“Whether we get him, whether we don’t, remains to be seen but we’re certainly in there with a shout.”
Glenn Hoddle insists we are ‘in with a shout’ of signing Liverpool’s unsettled German star Christian Ziege.