The Blues legend was relieved of his duties on Monday morning with the club ninth in the Premier League table - three points behind West Ham in the race for a European spot.
Lampard had supposedly earmarked Rice as his top target last summer, but the Blues failed to stump up West Ham's £80m asking price and the ever-present midfielder remained at the London Stadium.
Now, The Telegraph reports that West Ham do not expect the Blues to retain an interest in Rice now that Lampard is no longer at the helm.
The report claims that Lampard and the Chelsea hierarchy had differing views over signing the former academy starlet, and he will not make a return to Stamford Bridge unless incoming manager Thomas Tuchel wants to push ahead with a deal.
West Ham manager David Moyes has affirmed that whoever is in charge of Chelsea would have to fork out "Bank of England and Scotland" money if they want to prise Rice away from the London Stadium. body check tags ::