Alli moved to Premier League outfir Tottenham from Milton Keynes Dons, then in League One, in February 2015.
Former Spurs manager Redknapp was then in charge of QPR, who got relegated from the Premier League at the end of last season, and he has explained why he did not make a move for the 19-year-old midfielder.
“I never tried to sign him then because we were struggling all year and were just in for short-term fixes but it shames the recruitment networks at the top clubs — who could think further ahead — that they didn’t go in for him,” the Englishman wrote in The London Evening Standard.
Alli remains at MK Dons for the remainder of the 2014-15 season on loan and helped them get promoted to the Championship.
Redknapp stepped down from his managerial position at QPR in February 2015, with the London outfit eventually going down to the Championship at the end of the season.
Alli has been superb for Spurs so far this campaign and has established himself as a regular in the first team.
The youngster has also played four times for the England national team, scoring one goal in the process.