The Daily Record reports Fulham have carried a long-standing interest in the 27-year-old, a situation that first surfaced during the January window when Ipswich Town were also credited with monitoring him, though a move was always considered more likely to materialise in the summer.
Everton have since entered the picture too, with manager David Moyes weighing up a move as he looks to rebuild his full-back options following Seamus Coleman's departure and with Nathan Patterson also expected to leave Goodison Park.
None of that interest is likely to shift Celtic's position, however. Johnston made all five of Canada's appearances as the co-hosts reached the World Cup last-16 for the first time, form that has only added to his profile without changing the fundamentals of his situation at Parkhead: he is contracted, settled, and Celtic see no reason to negotiate unless a genuinely exceptional offer arrives.
Johnston has made close to 80 appearances since his £3m move from Montreal in January 2023, quickly establishing himself as first-choice right-back and one of Brendan Rodgers' most trusted defenders, despite a run of hamstring problems disrupting parts of last season.
He put pen to paper on his current deal in late 2024, with Rodgers describing his "phenomenal work ethic and attitude" at the time.
Fending off interest in key players from English clubs has become something of a recurring test for Celtic in recent transfer windows, and the club's approach with Johnston looks unlikely to differ: continue building the squad around him unless and until a fee arrives that makes turning it down genuinely difficult.
Moyes, in particular, is understood to have identified Johnston as one of several right-back options being weighed up at Everton this summer, alongside players from elsewhere in the Premier League and continental Europe.
Whether that interest develops into anything more concrete may depend as much on Everton's other business this window as on Celtic's willingness to negotiate, given the scale of investment already required elsewhere in Moyes' squad rebuild.