Spurs had a £7million bid rejected previously but Redknapp is reportedly willing to offer striker Robbie Keane as part of a cash plus player package.
West Ham manager Avram Grant is reluctant to let Parker go. The 30-year-old midfielder was in inspired form in the late stages of last season as the Hammers narrowly avoided relegation.
And West Ham co-chairman David Sullivan has promised supporters he will not Parker at any price when knocking back Spurs' initial offer.
With mega-spenders Manchester City having completed their transfer activity for the summer, few major purchases are expected on deadline day, with loan moves and swap deals more likely.