PSG coach Thomas Tuchel has been rumored to coach here for a few years now.
The Sun believes Lampard's form has been bad, but he is not instantly under threat of being shot.
Yet the sudden availability of Tuchel, following his axing by Paris Saint-Germain last month, has prompted several members of the board to take note of his availability in the summer.
After being beaten 3-1 at home by Manchester City last Sunday, Chelsea have lost four games in six.
Lampard is halfway through a three-year deal and has personally invested a total of over £220 million last year on six new players.
Tuchel led PSG to a Champions League title this year and was linked with Manchester United one year ago before Arteta got the job.
We understand the German, 47, is interested in the Premier League as his next move.