The 27-year-old has held talks with head coach Frank Lampard over his future in recent days after not featuring so far this season.
He has consequently sought assurances over his role in the team and while Lampard is not actively forcing him out of the club, Chelsea have a bloated squad and need to recoup some of the £220 million outlay on seven summer signings.
Paris Saint-Germain have expressed an interest in taking Rudiger on loan but Chelsea want a straight sale given he has two years left on his existing contract and they value the Germany international at around £20m.
Sources told ESPN earlier this month in September that Skriniar is Tottenham's first choice to strengthen the heart of their defence but Inter are continuing to hold out for a fee of €60m.
The two clubs are continuing negotiations but Spurs have repeatedly indicated they are unwilling to do business at that price and may turn their attentions elsewhere with Rudiger identified as one of several possible alternatives.
Any deal with Spurs for Rudiger is likely to be tough given Chelsea's reluctance to strengthen a direct rival for the Premier League's top four.
The Merseyside club were confident earlier this month that they had secured the 22-year-old on a season-long loan but a late change of heart at Chelsea has left the deal in limbo.
Tomori is viewed as a part of the Blues' long-term plan but he is unlikely to get regular first-team football at Stamford Bridge following the signing of veteran centre-back Thiago Silva.