Everton have lodged a formal appeal against their second points deduction for breaching the Premier League's financial rules, BBC Radio Merseyside understands.
The Toffees had a 10-point deduction reduced to six on appeal in February for the three-year period to 2021-22.
The latest appeal process must be concluded by 24 May, five days after the final Premier League game.
Sean Dyche's side sit 16th in the table, two points above the drop zone.
The Blues travel to face Chelsea in the league on Monday (kick-off 20:00 BST) aiming to distance themselves from the relegation zone.
Profit and sustainability rules (PSR) permit clubs to lose £105m over three years and an independent commission found Everton breached that by £16.6m for the three-year period to 2022-23.
The Merseyside club could yet face a further points deduction in relation to interest costs associated with the building of the club's new stadium at Bramley-Moore Dock, though that issue is unlikely to be resolved before the end of the season.
Timeline guide to Everton cases
24 March 2023: Premier League refers Everton to independent commission over alleged breach of financial fair play rules for the three-year accounting period ending with the 2021-22 season.
17 November 2023: Everton receive an immediate 10-point deduction after being found to have breached the Premier League's financial rules.
15 January: Everton and Nottingham Forest are charged for breaches of the league's profit and sustainability rules. The hearing has to be concluded within 12 weeks of this date, which is 8 April.
26 February: Everton's first penalty for breaching Premier League financial rules is reduced from 10 points to six after an appeal.
25 March: Hearing for Everton's second charge, relating to three-year accounting period ending in 2022-23, takes place this week.
8 April: Everton receive second points deduction of two points.
15 April: Everton lodge formal appeal over second points deduction.
19 May: The final day of the Premier League season, when Everton visit Arsenal (16:00 BST).
24 May: The latest possible date for an appeal hearing to be concluded.
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