The 27-year-old is understood to prefer a move that would see him stay in the Premier League, but the Blues are wary of offloading Rudiger to a direct competitor for the top spots in the division.
Remaining in England's capital would also be preferable for the defender, whose young family are feeling comfortable since his move to west London.
Inter's Milan Skriniar is Jose Mourinho's top target but Rudiger is also on the list at Tottenham.
The probable exit of Rudiger comes after Lampard signed Thiago Silva from PSG, which led to the Germany international dropping down to fifth in the central defensive pecking order.
For a time, it looked as though Fikayo Tomori would leave Chelsea, having had interest registered from Everton and Rennes among many others, but his exit has since been blocked.
Chelsea are allowing Rudiger to explore options with less than a week to go until the transfer window closes on October 5. The Blues are aiming to reduce numbers in their squad, which Lampard has recently admitted is oversized.
Alongside Rudiger's likely departure, Ruben Loftus-Cheek is looking for a loan move after missing the last three matchday squads and has interest from Aston Villa and West Ham.
However, his £150,000-a-week contract is a sizeable cost for both clubs, who are looking for wage contributions from the Blues to get a deal over the line.
There's also a need for the Blues to offload a full-back, with both Marcos Alonso and Emerson Palmieri seeing their futures in doubt after the signing of Ben Chilwell from Leicester.
Emerson looked set for Inter for some time, with a late moved expected from Antonio Conte's side, but Alonso's heated falling out with Lampard at the weekend has thrown his future into doubt.
Lampard is said to have lambasted the Spain international in front of the squad as the Blues went 3-0 down against West Brom and substituted him at half-time. Alonso watched the rest of the game from the team bus at The Hawthorns.
Furthermore, despite interest from Bayern Munich, Chelsea will block any attempts from the German giants to sign Callum Hudson-Odoi. The Blues have previously shunned attempted moves and will do so again having signed the 19-year-old to a long-term contract.
Still, Hudson-Odoi has recently had some concerns around game time in recent weeks, having only had two starts since football returned after the UK lockdown.
Chelsea's main transfer target late in the transfer window is Declan Rice but West Ham have yet to receive an approach for the midfielder.
The Hammers are determined to block any attempts of a cross-city transfer this summer, although the Blues are likely to retain a long-term interest in their former academy player.
Additional reporting from Benjamin Quarez, Kerry Hau and Ignasi Oliva.