Spurs have had bids turned down for the Hammers' talisman in the past, but with West Ham now facing up to life in the Championship a sale will definitely go through.
West Ham are determined to get a fair fee for the player, but Redknapp is wasting no time in making sure he is in pole position as far as the player is concerned.
Spurs' move for Parker is believed to hinge on the sale of Wilson Palacios to free up funds and space in the squad.
He said in the Sun: "Scott is combative, relentless, professional, modest and unbendingly committed. That's why he was voted the Football Writers' Player of the Year and why he is popular with most supporters of most clubs.
"Today he's likely to line up alongside Frank Lampard and Jack Wilshere against Switzerland. But when Steven Gerrard is fit, I don't see why Scott has to drop out. He could be a good fit in a midfield diamond. Scott is as versatile as any midfielder we have.
"He's not just a holding player. He can attack, score goals and play on either side of a midfield diamond.
"He is not flash at all. The car he drives is nothing special and he has a big knowledge of football, as do Gerrard and Lampard. I could see all three of them going into management one day.
"Scott played at Tottenham for West Ham last season, just hours after his dad had died. I don't want to say he's any better than anyone else for doing it because everybody reacts to things in their own way. But it tells you something about him and his love for football.
"And West Ham fans will tell you no one was more committed to their team last season."