Israeli mogul Levi Kushnir and Hong Kong-based Balram Chainrai have subsequently emerged as potential investors in the club and have attended Pompey's last two matches, Tuesday's 4-0 Carling Cup win over Stoke and Saturday's 0-0 league draw at Hull.
Another short transfer ban was imposed on the club at the end of August because of debts they owed, BBC Sport understands.
With seven players unavailable for the Stoke game, Hart was eager to sign Bopp, who he had managed at Nottingham Forest.
The 26-year-old, who was a free agent after being released by Crewe in the summer, had been training with Portsmouth for the last few weeks.
However, the Premier League refused to register the player because of Portsmouth's debts.
The transfer ban is the latest in a long line of off-the-field problems for manager Hart.
There was a delay in the players' wages being paid in September, while the club was on the brink of administration in August.
"A club needs to know where it is going and have a long-term plan," stated Hart ahead of Wednesday's 4-0 Carling Cup win over Stoke.
"I wouldn't like to go any further with that because I haven't had these conversations with the new owners. I would anticipate this would be in the next month."
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