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The club's record goal-scorer previously spent 19 months as manager at Stamford Bridge before being dismissed in January, 2021.
Lampard's last game in charge was Saturday's 2-0 league defeat at West Ham United, which kept Everton second-bottom of the table on 15 points after 20 games, above Southampton on goal difference, and two points adrift of the safety zone.
The match ended goalless with both sides hitting the woodwork.
He takes over a club four points above the relegation zone, and facing the distinct possibility of finding themselves competing outside top tier English football for the first time in almost 70 years,
Lampard did not get the best out of his squad this season despite the club spending more than 220 million pounds on new recruits.
Brighton had taken the game to Chelsea in the first half but fell behind after a defensive blunder in the 23rd minute when goalkeeper Mat Ryan fouled Werner in the area and Jorginho coolly converted the penalty.
Chelsea striker Tammy Abraham struck a 93rd-minute equaliser.
The reports did not name the players and Chelsea did not immediately respond to a request for comment.
Tammy Abraham, who is the club's leading goal scorer this season with 15 goals in all competitions, suffered an ankle injury, with Lampard having no update on his return to the side.
Lampard won 13 trophies in 13 years and became Chelsea's all-time leading marksmen with 211 goals from midfield during a decorated playing career at Stamford Bridge. But he has a lot to prove in his new role.
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