The People says Pompey are now confident of having a transfer embargo lifted before the January window opens as they pay off debts to rival Premier League clubs.
And Grant is eyeing target man Toni, 32, who has been frozen out at Bayern after a major bust-up with manager Louis Van Gaal and is available on a free transfer in January.
Grant used a midweek visit to Bayern's Champions League clash with his own former club Maccabi Haifa to check on Toni's availability and was told the player is keen to come to England.
But although Pompey will have cash available, Toni's current Bayern deal of £100,000 a week will come down significantly. West Ham were unable to thrash out a deal for Toni in the summer despite their sporting director Gianluca Nani being a close friend of the striker.