Dawson picked up his injury during a pre-season game against Bournemouth and Redknapp is pessimistic about their chances of facing Liverpool on 16 August.
"Ledley hasn't kicked a ball yet this season, so it is not looking great on that front at the moment," added Redknapp.
In the trio's absence, Dorian Dervite could get a chance to impress - the 20-year-old made his only competitive start in November 2006 - while Vedran Corluka and Tom Huddlestone can also play at centre-back.
Tottenham play Barcelona on Friday and Celtic on Sunday with strike duo Roman Pavlyuchenko (thigh) and Robbie Keane (groin) also doubtful. The club's first Premier League fixture is at home to liverpool on Sunday,
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