The Zimbabwe international was sold to City during the 2008 January transfer window for a figure quoted as £9 million, with £4 million of that to be paid up front and the remainder spread over the length of the player’s contract.
However, Portsmouth, who are fighting for their Premier League survival, are believed to be willing to take less than the full amount should City settle before the end of the season, according to a report in the Daily Mail.
The deal itself was problematic at the time, due to a knee condition that was revealed in Benjani’s medical.
UPDATE: Seemingly not though according to Portsmouth's official site:
Contrary to inaccurate newspaper reports today Portsmouth Football Club would like to make it clear that they are not in negotiations with Manchester City for an early settlement in connection with the transfer of Benjani Mwaruwari.
Both the terms of the deal and the transfer fee remain the same as in January 2008 when originally negotiated with Manchester City, who can confirm this.
Pompey announced at the time that Manchester City paid half the agreed £7.75m deal up front, with subsequent equal payments to follow after 25, 50 and 75 appearances.