Johnson has been the subject of interest from Chelsea, Liverpool and Manchester City already this summer and looks set to end his three-year stay on the south coast.
Manchester City were said to have made an £18 million bid for the former Chelsea defender earlier this week, but a fresh offer, thought to be in the region of £15m to £18m, has been made by either Liverpool or Chelsea.
Storrie has said that the club would not stand in the way of Johnson's chance to play Champions League football next season. Johnson is said to favour a move to Anfield over a return to Stamford Bridge following a disappointing spell in west London.
"I've know Glen a long while, from my West Ham days. When I re-signed him (at Portsmouth) we talked things over," Storrie said.
"He said, 'If one of the big four come in with Champions League football, would you stand in my way?'
"I told him I couldn't do that. Providing the deal is right for Portsmouth and Glen then we will look to try and do something in the right way.
"It is very hard to try and hold people back when they have a chance to play in the Champions League. I accept that."
When asked if an offer of between £15million and £18million had been tabled, Storrie replied: "You may not be a million miles away from the mark."
The main stumbling block to Liverpool's approach is the financial backing needing to launch a bid. Rafael Benitez has been told he must offload players before he can look to bring in fresh faces this season.
Johnson impressed Benitez with his attacking play down the right flank last season and played a key role in England's 6-0 win over Andorra in midweek, but his arrival would not leave the Liverpool manager with the spending capacity to further bolster this squad.
Bayern Munich, meanwhile, have also enquired about the 24-year-old but Johnson is thought to prefer to stay in England in the build up to next summer's World Cup finals in South Africa.