The pressure on Lampard has intensified after Tuesday's loss to Leicester, a fifth defeat in their last eight games.
It is believed Lampard will be given time to turn things around, but should result continue, Abramovich will make a change in the dugout.
RB Leipzig manager Nagelsmann is a potential target after his excellent work in Germany.
However, Sky Sports states the Blues would have to until the end of the season to bring Nagelsmann to Stamford Bridge.
Max Allegri and Thomas Tuchel, both unemployed, have been linked with the job and both would be interested.