The Hoops have so far signed just one player, but Johnstone expects them to be busy in the coming weeks.
Celtic manager Brendan Rodgers
Brendan Rodgers' men have made just the one signing so far this summer, with Moussa Dembele arriving from Fulham, while Kristoffer Ajer also linked up with his new team having agreed a move in February.
Moussa Dembele is Celtic's only signing of the summer so far
But with former Rangers man Johnstone anticipating a stronger title challenge from their Scottish Premiership rivals this season, he has suggested that the Hoops could well be busy before the deadline.
"Celtic know they have got a fight on this season because Aberdeen and Hearts will be stronger and Rangers have certainly improved a lot already," he told the Evening Times.
"Brendan Rodgers will know he has to bring in a couple of quality players and it wouldn't surprise me if he spent two or three million to strengthen his squad before the start of the league season."
With an already large squad to work with, Rodgers may fear that adding more players before he has managed to move any on will make his task of maintaining harmony amongst the side much tougher.
However, after suffering a defeat to Lincoln Red Imps in the first-leg of their Champions League second qualifying round tie, the Northern Irishman will surely feel that some areas of the squad need improving if the Bhoys are to confidently see off any team that wishes to challenge for their place at the summit of the Scottish game.