Parker, who recently refused to sign a new enhanced long-term contract offer with the Hammers, has been a Spurs target for a while now and boss Redknapp is keen to secure the players services ahead of the shutting of the transfer window on Tuesday.
Earlier this summer a £8million pound offer was turned down by the Hammers but financial difficulties at Upton Park have made Parker's signature a possibility according to a report in the Daily Mail.
The article claims co-owners David Gold and David Sullivan may now have to sell the star player against their wishes.
Hammer's boss, Avram Grant recently commented that: "As far as I know the club wants him [to stay] for a long, long time and Scott wants to stay here so he's part of our project for the next year."
Another player who could be on his way out of Upton Park is Hammers front man Carlton Cole.
A number of clubs including Liverpool are interested in the striker with a loan deal being an attractive option, as the club look to downscale their wage bill.