Administrator Trevor Birch said last month that Pompey's high earners must be off the wage bill by August 10 or there would be no chance of rescuing the stricken club.
And today he revealed Israeli defender Tal Ben Haim - reportedly on £36,000 per week - had left Fratton Park after reaching a compromise agreement.
Birch also expects to make an announcement on the future of midfielder Liam Lawrence, the last remaining senior player on Pompey's books, within the next 24 hours while talks are ongoing with former striker Kanu after he left with a year remaining on his contract.
Therefore, negotiations with former owner Balram Chainrai's company Portpin over their takeover should take place over the next few days.
In a statement, Birch said: "I am pleased to announce we have reached a compromise agreement with Tal Ben Haim, who will now leave the club.
"We expect to make an announcement on Liam Lawrence's future later and, whilst the situation with Kanu has not yet been resolved, we are cautiously optimistic about our prospects.
"The progress we have made over the past 24 hours means there is now a much better prospect of meeting the conditions of the CVA (company voluntary agreement), completing the sale of the club and avoiding liquidation.
"As a result, we will now push on with our negotiations with Portpin, with a view to finalising a deal in the next few days.
"There is still more to do, and the club's future is not yet guaranteed, but we're in a stronger position and will now take some additional time to try to conclude matters."
It also emerged on Thursday that Portsmouth Council have agreed to loan rival bidders, the Pompey Supporters' Trust, £1.45million towards their proposal to buy the club.
Fratton Park staff had been told to be prepared to clear their desks if the deadline was not met.
However manager Michael Appleton, who is working with a squad made up of trialists and youngsters, told The News: "I haven't cleared my desk but there isn't much in there, to be fair.
"My gut instinct is that the club will be fine.
"If we get to a situation where I am able to do work and bring players in, I would like that as quickly as possible.
"That would give me a few days before the season starts. But, obviously, it's so important that the club survives and that we are competitive for next season."
Portsmouth will begin the npower League One campaign next weekend on minus 10 points and are due to start their season with a Capital One Cup clash against Plymouth on Tuesday.