Former Watford owner Laurence Bassini has submitted a formal offer for Portsmouth, but his bid is not considered a "game changer".
The Portsmouth Supporters' Trust and Portpin are both vying for control of the troubled League One club.
They are currently satisfying the Football League of their suitability to take over the administration-hit side.
Meanwhile, ex-Pompey owner Sulaiman Al Fahim, who expressed interest last week has still not provided proof of funds.
Al Fahim had a short-lived spell as owner of Portsmouth in 2009 before selling to Ali al Faraj but has still not distributed funds into a UK bank account.
Pompey have been in administration since February, with debts of about £61m.
They have both had Company Voluntary Arrangements agreed with creditors of the club but are yet to convince the Football League of their suitability.
The Football League is keen that Pompey avoid going into administration for a third time in as many years.
Both Balram Chainrai's Portpin and the PST, led by Iain McInnes, are also undergoing the Football League's fit and proper person test.
On Friday the pair were given an extension by administrator Trevor Birch to satisfy the Football League with their bids for the club.
In particular the Football League is concerned about the PST's commitment to honour compromise agreements with former players of the club - totalling around £8m.
The main issue the Football League has with Portpin is the amount of debt it is proposing to carry over into the new business.
This is one of the reasons the Football League imposed its last 10-point penalty on Pompey in July, something it later suspended when Portpin pulled out of the bid.
Administrator Trevor Birch is yet to chose a preferred bid and will still chose the best deal for creditors, although he will also be led on advice by the Football League.
There could be a decision as early as Tuesday afternoon or as late as the end of the week.