Coventry and owners SISU will appear at the High Court in London on Friday to contest an administration order brought against them by Arena Coventry Limited.
ACL, who manage the Ricoh Arena on behalf of joint-owners the Alan Edward Higgs Charity and Coventry City Council, claim they are owed more than £1.3m in unpaid rent dating back a year.
The ongoing row has led to Coventry having their bank accounts frozen, while earlier this month City were also placed under a transfer embargo after they again failed to file their annual accounts on time.
The club are currently eighth in League One and just three points off the play-offs, but a 10-point penalty would effectively end their promotion hopes.
Former Falkirk boss Pressley, appointed manager of City two weeks ago, said: "My biggest concern is for the players and supporters because it's been 39 games of hard work and following the team. It's them who suffer most.
"I desperately hope we find a solution and continue challenging for those play-off places. We can only wait until we hear the verdict and continue to prepare for Saturday's game in the hope we can still go on and gain promotion.
"The players and the supporters are the ones who really suffer out of this, that's why I'm desperate for some form of solution."
On the possible 10-point deduction, Pressley added: "It becomes mission impossible in terms of promotion but it's certainly not 'season over'. There's always something to play for and one of the things is in this football club."