Sarri has come under increasing pressure in recent months after several below par performances by the team in recent weeks.
Going into the final few weeks of the season, the Blues are in danger of missing out on a place in the top four.
With eight games remaining they are in sixth place and face an uphill task to gain ground on the likes of Arsenal and Manchester United.
They do have the bonus of a chance to win the Europa League which would qualify them for next season’s Champions League that way.
But there is a growing feeling the Italian is not a natural fit for the club and he could even be gone before the season end.
And the club are focussing their attention to Lampard or Espirito Santo to steady the ship, according to The Mirror.
Reportedly near the top of the new shortlist is the Wolves boss, who has attracted plenty of praise for his work since taking charge of the club in 2017.
Promotion from the Championship as champions has been backed up with some excellent performances in the Premier League this season.
Wolves are favourites to finish seventh and are looking forward to a trip to Wembley to play Watford in the FA Cup semi-final.
Chelsea all-time record goalscorer Lampard would surely be the fans favourite to replace Sarri, however.
Their former midfielder has led Derby to eighth in the Championship in his first season in management, one point outside the play-off places with a game in hand.
Abramovich is reportedly not keen on sacking Sarri before the season end but may have to if results to not pick up or the club are knocked out of the Europa League.
The Blues have been pitted against Slavia Prague in the quarter-final and have on paper the easier side of the draw to reach the final.
Should they make it there, they could ironically have to play Sarri’s former team Napoli, could could conceivably get him the sack at Stamford Bridge by winning.
Chelsea bosses had thought to have pinned their hopes on landing Zinedine Zidane before he returned to Real Madrid a couple of weeks ago.
It remains to be seen whether Sarri can survive the onslaught that is sure to face him with every passing game where the team struggles.