Kehl, 46, left Dortmund last month after four years in charge of the club's football operations, a spell that included a Champions League final appearance in 2024 and the signings of Nico Schlotterbeck and Serhou Guirassy.
The role would sit alongside that of Johan Lange, Spurs' current co-sporting director, who has faced significant criticism from supporters over recruitment decisions that have contributed to the club's relegation battle, reports The Sun.
The position became available in February when Fabio Paratici departed for Fiorentina just four months after his appointment.
Sources in Germany suggest Kehl had also attracted interest from Hamburg and Wolfsburg, where he considered remaining in his home country.