The Argentine has already spoken to the club and we understand he has provided a break-down of the squad. His chief concern is said to be a lack of pace, especially in defensive areas.
Bielsa has let it be known he is interested in taking the job but has reservations over the current squad being able to implement the high energy style of play that is his trademark.
If guarantees are not given over a plan to address his concerns, sources say there is a chance Bielsa will walk away from talks.
It remains to be seen whether the Merseyside club try to persuade Bielsa or move onto other targets.
Key figures within the Everton hierarchy remain admirers of their previous manager Sam Allardyce, who has held initial talks with the club over replacing Lampard.
There is a feeling at Goodison that Allardyce’s experience in guiding relegation threatened teams to safety offers the club with a strong chance of avoiding the drop.
Sean Dyche is out of work, but there is a reluctance from the Everton board to move for the ex-Burnley boss.
Allardyce spent just six months with Everton in 2017-2018 after being appointed by Farhad Moshiri to replace Ronald Koeman – with the club in danger of being relegated – and ended up guiding the Toffees to an eighth place finish.
But despite being handed an 18-month contract, he was sacked at the end of the season, with fans not won over by his defensive style of play. Since leaving Everton Allardyce had a brief stint in charge of West Brom in 2020-21, but has not managed a team since.
Everton will need another manager who can help them reach safety after finding themselves 19th in the table after picking up 15 points from 20 games – with just three wins, the lowest of any side.
The club confirmed the sacking of Lampard on Monday evening after Sportsmail broke the story earlier in the day.
‘Joe Edwards, Paul Clement, Ashley Cole and Chris Jones have also left the Club. Alan Kelly will remain as goalkeeping coach.
‘Everyone at Everton would like to thank Frank and his coaching staff for their service during what has been a challenging 12 months.
‘Frank and his team’s commitment and dedication have been exemplary throughout their time at the Club, but recent results and the current league position meant this difficult decision had to be taken. We wish Frank and all his backroom team well for their future in the game.
‘The Club has started the process to secure a new manager and will provide updates on the appointment in due course.
‘Paul Tait and Leighton Baines will take training until a new manager is appointed.’
The former Chelsea and Derby boss was told his 357-day spell in charge had come to an end during a phone call with Moshiri, Everton’s major shareholder.
Lampard had been in discussions with Moshiri, Chairman Bill Kenwright and Kevin Thelwell, Everton’s Director of Football, on Sunday after a 2-0 defeat at West Ham – Everton’s 11th loss in their last 14 games in all competitions.