Trotters boss Gary Megson is apparently considering a £1.5 million bid for the striker, who has slipped way down the pecking order at Eastlands. Benjani's only appearance so far this season has been as a second-half substitute in the League Cup tie against Scunthorpe United.
The player has recently recovered from a thigh injury. He would also be available in January as Zimbabwe have not qualified for the African Cup of Nations.
Portsmouth were thought to be interested in taking the player back to Fratton Park, but the sacking of manager Paul Hart this week means that situation has now changed.
Wigan Athletic and West Ham United are also reportedly monitoring the striker's situation.
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