Redknapp, who was named QPR's new boss on Saturday, has made defensive reinforcements one of his top priorities at Loftus Road.
Rock-bottom QPR have struggled defensively this season and have conceded 26 goals so far this term, including three in the defeat by Manchester United.
Redknapp has made a new central defender a priority in the January transfer window and Dawson is thought to be his top target.
Dawson came close to joining QPR in the summer before he eventually turned down the chance to move to Loftus Road.
However, Redknapp, who worked with Dawson at Spurs, will be hoping he can persuade the player to reconsider a switch to QPR in the new year.
Dawson has found himself out of favour under Andre Villas-Boas this season, making just eight appearances in all competitions this season and he could be tempted to move on in search of regular first-team football.