The News understands the Blues would not stand in the right-back’s way, should a club make a move for his services before August 31.
Johnson has been out of the picture in the past two games, as he serves a three-game ban for a controversial red card in Carabao Cup loss at Millwall.
His only league action so far this term arrived as a late sub in the opening-day win at Fleetwood Town.
Kieron Freeman has established himself as Cowley’s first-choice, since his summer arrival after leaving Championship Swansea City.
Johnson has a year to run on his existing agreement, with Pompey holding an option to extend that stay by a further 12 months.
The 24-year-old has shown himself to be a dependable option since arriving from Accrington Stanley last summer.
The former Middlesbrough trainee was among Pompey’s most consistent performers amid 46 outings in the 2020-21 campaign.
That was recognised as he finished third in the The News/Sports Mail player of the season vote, behind Ryan Williams and Craig MacGillivray.
Johnson perhaps lacks the forward-thinking attributes to be a natural fit in Cowley’s game idea, however.
The Pompey boss is also in the market for a right-sided defender who can operate centrally and give him the option to move to a back three, something he feels he currently lacks.
Cowley missed out on TJ Eyoma this week as the Spurs man moved to League One rivals Lincoln City.
A message from the Editor, Mark Waldron
The News has launched a subscription offer which gives you unlimited access to all of our Pompey coverage, starting at less than 14p a day.
You can subscribe here to get the latest news from Fratton Park - and to support our local team of expert Pompey writers.