Rs owner Tony Fernandes is said to be unlikely to want to sack Redknapp - but will consider his options if the west London's side woeful run of form continues.
QPR are rock bottom of the Premier League table after seven games and have won just once so far this season.
It is another former Tottenham Hotspur boss that Fernandes could reportedly turn to if he does wield his axe, however, as first-team coach Glenn Hoddle is touted by the Mirror report as favourite to replace 67-year-old Redknapp, with club sources cited as confirming the rumour.
Les Ferdinand, another former Spurs coach who has re-joined QPR as head of football operations, has also been suggested as a possible Redknapp replacement.
Interestingly, bookmakers see Sherwood as the front runner to become the Rs' next permanent manager, contradicting the Mirror's report.
According to Oddschecker, the 45-year-old is as low as 2/5 to take up the reins at Loftus Road, with Tony Pulis and Gianfranco Zola both ahead of Hoddle.