It seemed likely that the 24-year old would join Liverpool earlier this week but Johnson's former club have come forward with a slightly increased offer.
Portsmouth have come to terms with the fact Johnson will be leaving the club this summer but his destination is still up in the air.
"The matter will come to a conclusion at the beginning of next week. I do not have a preference over the move, it is up to Glen," said Pompey chairman Peter Storrie.
"The deals are almost identical so it really is down to him and what club he prefers, which one is going to pay him more money.
"Glen wants to play regularly in the Champions League, he has got himself back in the England side so I understand that. Sometimes you have to be fair to players."