The England U21 international has impressed on loan in the Championship with Brentford, scoring three goals in 21 games for the west Londoners.
Redknapp watched Pritchard in the Bees' 3-1 win against Blackburn on Saturday and is considering making a move for the youngster in January.
The Spurs academy graduate is due to remain at Griffin Park until the end of the season, but there is a break clause in the deal.
Brentford are keen to make the move permanent, but face competition from Premier League trio QPR, Burnley and West Brom.
The 21-year-old made his Tottenham debut in May, appearing as a late substitute in the 3-0 home win against Aston Villa.