Having steered the club to fourth in the Premier League last season to secure a place in Europe's premium club competition, Redknapp is looking to take advantage of chairman Daniel Levy’s generosity this summer.
According to the Mail on Sunday, the Spurs chief will keep tabs on the highly-rated South African midfielder Pienaar while working for the BBC at the World Cup.
Pienaar, who impressed last term with seven goals, is entering the final year of his contract at the Merseyside club and is keen to settle his future.
Redknapp's other target is believed to be Bolton captain Cahill. The former Aston Villa centre-back was linked with a move to Arsenal during the last campaign but could be lured to White Hart Lane with the prospect of playing in Europe.
The 24-year-old Englishman would cost Spurs as much as £15 million, according to reports from The Mirror.
Cahill was in line to make the England World Cup squad before injury disrupted his season, after a blood clot was discovered in his arm in February.
However, Redknapp with a significant transfer war-chest at his disposal the hefy price-tag will not deter him as he aims to give Spurs some added strength in depth heading into a maiden Champions League campaign.
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