The News understands a homecoming for the midfielder is looking increasingly unlikely after his exit from Accrington Stanley.
The 25-year-old from Denmead has repeatedly been linked with a switch to Fratton Park and is a free agent this summer.
Butcher is a player who has interested Danny Cowley, but the Pompey boss appears to have other priorities at present.
There are still a stack of clubs keen on landing the former Cowplain School pupil, including League One rivals Bristol Rovers and Fleetwood.
Butcher made 36 appearances for Accrington last season, bagging four goals - including a finish against the Blues in the 2-2 draw at the Crown Ground last October.
Pompey have followed his progress closely and showed strong interest last summer.
But with Butcher under contract, playing a fee for a midfielder never looked on the cards - until cash was freed to land Joe Morrell in the final weeks of the transfer window.
Now the former Bournemouth man is out of contract representing good value, as he prepares to find a new home next term.
That has put him on Pompey’s radar, but Cowley appears set to look elsewhere more actively as the transfer window opens on June 10.
With 10 players contracted and options taken up on a further four men from last term, there is still a lot of work ahead to assemble a squad capable of competing for promotion.
The midfield department is one area where Pompey are relatively well stocked with Joe Morrell and Ryan Tunnicliffe already contracted.
They have been joined by Louis Thompson and Jay Mingi, with options taken up on the duo.
Cowley would still like to add another body in the middle of the park, however.
An option with more defensive instincts is what the Pompey boss is looking for in that area.
As well as Butcher, the Blues have also been linked with moves for St Mirren’s Ethan Erhahon and Oxford United’s Alex Gorrin in that department.