Croatia international Kranjcar played under former Spurs boss Redknapp at White Hart Lane after being brought to North London by the manager from Pompey in 2009.
He departed for Ukraine last summer after falling down the pecking order at Spurs, with injuries hindering his progress.
Now Redknapp is understood to be targeting another reunion with the 28-year-old attacking midfielder.
QPR have already struck in this month's transfer market as they look to escape relegation from the Premier League this season, bringing in Loic Remy from Marseille.
Redknapp is also understood to be interested in signing Sissoko but Sky Sports understands the Toulouse midfielder's preference is to join Newcastle United.
Meanwhile, QPR's pursuit of Peter Odemwingie remains ongoing and the West Bromwich Albion striker is said to be keen on a move but there has been no new bid.
However, QPR are preparing an improved offer for another West Brom player, Jonas Olsson, in their continued chase of the centre-back.