Spurs boss Jose Mourinho is keen to add a central defender to his squad before the window slams shut on 5 October and Rudiger has emerged as a possible signing.
The Germany international has fallen out of favour at Stamford Bridge under Frank Lampard, yet to make an appearance for the Blues this season and only making it onto the substitutes’ bench once.
In his place, Kurt Zouma, Andreas Christensen, Thiago Silva and Fikayo Tomori have all played at centre-back for Chelsea so far this campaign.
Sky Sports report that Tottenham are keen to take advantage of the situation and that the player would be keen on a loan move away from Chelsea, with the European Championships next summer and a place in the Germany squad on the line.
However, Chelsea are unlikely to want to strengthen a Premier League rival, with Spurs possible rivals to the Blues for a Champions League place at the end of the season.
Chelsea found themselves 3-0 down to newly-promoted West Brom on Saturday, fighting back to earn a 3-3 draw, but the pairing of Christensen and Silva looked far from secure.
Christensen has already been sent off this season, in the 2-0 defeat to Liverpool, and Rudiger could push for a return to the first team if Chelsea don’t improve at the back.
The former Roma man also complained of suffering racist abuse when Chelsea played Tottenham last season, so Spurs will not be his destination of choice if he is to leave Stamford Bridge.