Orient drew 2-2 at Swindon in their final match of the season on May 3 as they were relegated to League Two after a disappointing campaign.
Club president Francesco Becchetti is reportedly entertaining offers for the club, but is understood to have ordered the squad to continue training rather than being allowed to go on holiday.
Orient striker Shaun Batt tweeted a cryptic message on Monday afternoon suggesting the decision has not gone down well with the club’s playing staff.
He wrote: “Seasons finished, there’s no more games, yet were in training mon/tues/wed/thurs till the 24th May. #Buzzing #NoFamilyHolidaysThisYearBoys.”
Orient’s decline has been spectacular since they missed out on a place in the Sky Bet Championship following a League One Play-off final defeat on penalties to Rotherham 12 months ago.
Bechetti acquired the club from previous owner Barry Hearn last July and two months later former manager Russell Slade resigned.
Current boss Fabio Liverani became Orient’s fourth different manager this term when he was appointed in December with the club just outside the relegation zone.
But the former Italy international was unable to halt the slide as the club ended the season in 23rd place on 49 points – 37 less than last season – resulting in their relegation to League Two.