The towering centre-back would set Tottenham back around £10 million but it is a price they are willing to pay, according to a report in the Sun, after Redknapp has seen his three senior centre-backs sidelined.
Michael Dawson is unlikely to feature until September due to Achilles trouble, Jonathan Woodgate is to undergo surgery on a groin injury while Ledley King continues to be plagued by his long-standing knee problem and has hardly featured in pre-season.
Samba, a Congo international, joined Rovers from Hertha Berlin 2007 for £400,000 and has been a success at the club, mainly playing as a ball winning centre back but more recently performing manfully at the other end as a makeshift striker.
Redknapp initially felt he could ride out the injury crisis by promoting Dorian Dervite to the first team but after watching the 21-year-old struggle against Celtic in a pre-season friendly has decided that experienced cover is essential.
Meanwhile, Redknapp appears to have missed out on the signing of former Chelsea winger Arjen Robben from Real Madrid.
Robben looked set to return to the Premier League with Tottenham after slipping down the Bernabeu pecking order after the arrival of Cristiano Ronaldo and Kaka.
However, Robben, who struggled to hold down a first team-place in Madrid even before this summer's extraordinary spending, said: 'With all the respect in the world, I have decided not to join Tottenham.
'I hope to achieve a lot with Real Madrid. The only thing I would consider is a move to another club in the Champions League.'