Saracens were docked 35 points and dealt a £5.36million fine last November after they were found to have broken the £7million salary cap for the past three seasons.
A summit of Premiership Rugby Limited chief executives was held in London on Tuesday, where it is reported that Sarries were issued with an ultimatum.
According to reports, Sarries were told to hand back the titles won in the three years in which they have breached regulations or face expulsion from the top flight.
It is understood that the club is struggling to keep within the salary cap again this season, though they are working to find a solution.
Players and staff have been called in for an emergency meeting.
- Nigel Wray steps down as Saracens chairman with 'immediate effect'
- Saracens appoint lawyer Neil Golding as new club chairman
Ed Griffiths has been re-appointed chief executive to oversee the necessary changes and he will be assisted by Neil Golding, who has taken over as non-executive chairman.
Golding is described as a "highly experienced and respected lawyer" and specialises in disputes, litigation and arbitration at Freshfields Bruckhaus Deringer.
"I am joining the club at a time of significant change," said Golding earlier this month.
"We, as a board, are strongly committed to introducing new robust processes and working together with other Premiership Rugby stakeholders in the best interests of Saracens and English rugby."
Griffiths has confirmed that Saracens must reduce their wage bill and, alongside director of rugby Mark McCall, is identifying players to be trimmed from the squad.
Wales full-back Liam Williams' departure for Scarlets that is due to happen at the end of the season is could be brought forward, while Richard Wigglesworth, George Kruis, Juan Figallo and Michael Rhodes face uncertain futures.
Saracens host Racing 92 in the Champions Cup at the Allianz Arena on Sunday.
The salary cap explained
Premiership Rugby introduced the salary cap in 1999 with the twin aims of ensuring a level playing field and maintaining a competitive, growing and financially sustainable league, ie preventing the clubs from the pitfalls of over-spending.
The cap was increased from £6.5m to £7m ahead of the 2017-18 season and will remain at this level until the end of the 2019-20 season. The ceiling includes dispensation for academy and injured players and effectively raises the possible spend to around £9m.
Additional reporting by the Press Association