The 55-year-old has had a tough start to life at Ibrox, losing two and drawing one across his three games since their 2026-27 campaign began.
Rangers are already five points behind arch-rivals Celtic in the race for the Premiership title, and have already suffered two major injury blows.
McInnes confirmed on Wednesday that left-back Tuur Rommens faces up to eight weeks on the sidelines after sustaining a groin strain in their 2-1 defeat to Hibernian.
While Youssef Chermiti, who was of interest to Galatasaray, is also ruled out for a "significant period of time" after suffering an anterior cruciate ligament (ACL) injury in the same game.
The Glasgow club have already made nine additions so far this summer, two of which are defenders: Olwethu Makhanya from the Philadelphia Union and Ross McCrorie from Bristol City.
McInnes, however, insists the club need more depth. "Strengthening defensively, strengthening in wide areas was a priority. But obviously losing a player of Youssef's ability, we need to look at that one as well," he told reporters.
"We don't have an array of options defensively. We don't have a left-footed defender in the building, and we're keen to try and get that resolved as quickly as possible.
"I do think that with the numbers we've got there, we are playing with fire, and there are a couple of defenders being injured.
"The good thing is we've got the ability to react to it, and hopefully we can react positively."