The People says Aussie Viduka, 32, has been frozen out of the first team since Kevin Keegan's return and is keen to leave Tyneside.
Redknapp registered his interest in the player when Sam Allardyce was still the Toon boss and the Pompey chief knows Viduka will be available for a small fee.
Redknapp wants a targetman striker to play alongside Jermain Defoe and believes Viduka fits the bill.