Nuttall is described as being a 'cult figure' at Blackburn - for whom he has scored eight goals in 34 games since his 2017 move from Aberdeen.
But only 15 of those outings have arrived this season - two as a starter - and the newspaper states that he 'needs to play every week'.
And a move to Portsmouth - who could lose strikers James Vaughan and Omar Bogle to their parent clubs this summer - could provide Nuttall the opportunity to do so.
The 22-year-old - who began his career at Manchester City - is under contract with Blackburn until 2021, so Portsmouth may need to pay a fee to sign him.
Strikers Brett Pitman and Oliver Hawkins are each tied to Pompey - who could return to the Championship next season - for another 15 months.
Would the Blackburn striker be a good addition for Portsmouth?