The Sun says Pompey boss Harry Redknapp wants to capitalise on his side's FA Cup success by strengthening his squad.
And he believes he can persuade Chelsea to take a loss on out-of-favour Wright-Phillips.
Redknapp, whose side are in the UEFA Cup for the first time next term, had planned to sign Wright-Phillips and Jermain Defoe for Newcastle had he taken the Toon job in January.
But, after opting to stay at Fratton Park, he snapped up Defoe and now wants to make it a double by landing England international Wright-Phillips.
However, Pompey will face competition from Newcastle who are still interested in the player.