The Norwegian led New York City FC to MLS Cup success in 2021 and took over at Liege earlier this summer.
Johnston has had injury issues preventing him from staking a claim for a regular starting berth.
The 23-year-old has started just 16 matches across the past three seasons and has the likes of James Forrest, Liel Abada, Jota ahead of him in the pecking order, while Daizen Maeda and Kyogo Furuhashi can also be used wide.
Highly thought of at Celtic Park, a loan would allow Johnston to get a run of first-team games.
He could be the first of a number of players who could exit between now and the end of the transfer window.
Christopher Jullien was close to a switch to Schalke 04 earlier in the window, while Albian Ajeti is surplus to requirements.
Osaze Urhoghide and Liam Shaw had loan spells last season. The same could happen once more, as it could for Dane Murray, Johnny Kenny and Scott Robertson.
Manager Ange Postecoglou has spoken of his need for a decent squad to handle the challenges the club will face.
Celtic will compete on four fronts with a condensed fixture list, fitting six Champions League group stage fixtures before the World Cup gets underway in Qatar.
After the Blackburn Rovers friendly earlier this month he noted the stress it will add to the squad and why he was keen to add to the squad as he did with Aaron Mooy and Mortiz Jenz.
"We had a pretty hectic schedule last year," he said. “The reality is we’ll play close to 60 games.
"Champions League on a weekly basis will add stress to the squad which is why I’m keen to bring in a couple more, to make sure we’re strong and robust.
"Last year it affected our ability to perform at a really high level. I don’t think it’ll be a bigger squad, just more robust with quality.”