Redknapp is preparing to test the North London club's resolve as he readies his side for life back in the Premier League, The Metro reports.
Townsend enjoyed an impressive start to last season, earning himself an England call-up, but injuries and loss of form have seen him fall down the pecking order at Spurs.
However, new Tottenham manager Mauricio Pochettino is said to have been impressed with the winger's attitude since his arrival at the club, and is reportedly reluctant to sell.
Rangers have already completed deals for Rio Ferdinand, Steven Caulker and Jordan Mutch, and look likely to complete a deal to bring Juventus' Mauricio Isla to Loftus Road on loan.
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