Boss Antonio Conte is keen to bring in more reinforcements in the winter window but the budget for January at Tottenham is likely to be tight.
The Tottenham boss wants to bring in a new centre-back into his squad in January or the next summer transfer window.
Several profiles are being studied and Hincapie is a player the Italian coach admires and he is keen to sign him.
And according to Italian outlet Tutto Mercato, the north London club are weighing up making an offer for him.
Conte is in discussions with football director Fabio Paratici and the Leverkusen defender is on their shortlist.
However, it is unclear whether they are planning to make a move for him in January or wait until the summer.
Hincapie is also on the wish list of several big Italian clubs such as AC Milan, Juventus and Napoli.
But Tottenham have the funds to financially outmuscle the Serie A giants if Hincapie is keen to move to England.