Boss Mauricio Pochettino wants to pile the pressure on error-prone Hugo Lloris with the France World Cup winner struggling for form.
Onana, 22, has impressed for the Dutch giants having played in all 10 of the club's league matches this season.
Marseille wanted to land him in the summer but Ajax refused to cash in on the talent.
Onana was then rewarded with a new contract until the summer of 2021 to prevent him from leaving for the French side.
But the lure of moving to London to sign for Mauricio Pochettino may prove too much for the Cameroonian international.
Dutch publication VI claim that Spurs will make their move in January to pile the pressure on Lloris.
The club's No1 has been heavily criticised by fans after his last howler was the catalyst to Spurs dropping two crucial points in the Champions League.
He received a straight red card in his reckless lunge against PSV Eindhoven before they went to concede a late equaliser to leave Spurs with an uphill task to qualify from their group.
One fan fumed after the game: "Sell Lloris. He's finished."
Another wrote: "Sell Lloris ffs!!! Constantly making mistakes!"
Last month the 31-year-old was banned from driving for 20 months after admitting to drink driving.
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