Former Manchester United starlet Rossi, who is understood to be valued at around £8 million, is being lined up by Redknapp and Spurs chairman Daniel Levy, according to The News of the World.
Although the north London club still have the option of signing Huntelaar from Milan before the transfer window shuts on Tuesday, the newspaper claims they are not yet wholly convinced about the Dutch striker's suitability.
Huntelaar enjoyed an outstanding four years with Ajax but has found life tougher in spells at Real Madrid and Milan, and is currently available on a season-long loan.
However, the possibility of snaring Italian Rossi is said to be of particular interest to Levy.
Rossi showed promise in limited opportunities at Old Trafford, and endured a frustrating loan spell with Newcastle United before finding his feet in Spanish football with Villarreal, for whom he has been a consistent goalscorer.
And having qualified for the group stage of the Champions League, Spurs could make a late bid for Rossi to boost their forward armoury. Such a move might, though, necessitate or precipitate the off-loading of Newcastle target Robbie Keane.