The Blues are no nearer to agreeing a deal for the defender with time ticking down on his contract which ends this summer.
The News understands Burgess, who has been in the best form of his Fratton career this season, has options to move elsewhere - including on the continent.
Pompey made the 28-year-old an offer when initial talks took place but there has been no developments since.
It appears Burgess now looks likely to take a pragmatic approach to his seeing how his future will pan out, by letting his deal wind down and seeing what’s on the table.
An exit for the former Peterborough man would be a blow for Kenny Jackett after emerging as one of his side’s outstanding performers this season.
After enduring highs and lows in his five years at PO4 he has become as big fans’ favourite with a departure sure to cause reverberations among supporters.
Burgess’ displays amid 43 appearances made him one of the key contenders to pick up player of the season honours before football was suspended.
He has also earned plaudits for his voluntary work in the community since the stoppage to the English game.
Burgess suggested earlier this month discussions were up in the air with the uncertainty surrounding football amid the coronavirus crisis.
He stated on that occasion clubs like players are waiting to see ‘what the landscape is going to look like’ before moving forward.
Pompey have eight players out of contract this summer with Burgess a free agent along with Lee Brown, Brett Pitman, Oli Hawkins, Brandon Haunstrup, Luke McGee, Adam May and Matt Casey.