Anderson, Robinson expected to be fit for England's Ashes bid
Anderson strained his groin while on Lancashire duty and Robinson suffered an ankle issue playing for Sussex earlier this month.
The pair will remain sidelined when England host Ireland at Lord's in a four-day match prior to the first Ashes Test.
The five-match series against Australia begins on June 16, but McCullum is confident Anderson and Robinson can return in time for the opener in Birmingham.
"For the first Ashes Test, I think they should be fit," McCullum said on Monday.
"They won't be fit for this one against Ireland. We'll just have to monitor it over this next sort of while, but we've got some great options right throughout the squad.
"When I first took over this job, people said there wasn't much depth in English cricket and I disagree with that completely.
"I think there is an immense amount of depth and we've got plenty of good options throughout the squad."
England already have fitness concerns over a number of other bowlers, with Jofra Archer and Olly Stone struggling with elbow and hamstring problems respectively.
With Anderson and Robinson ruled out, Stuart Broad will lead the bowling attack against Ireland but Mark Wood will have to be assessed before a final decision is made on his fitness.
"He is bowling over there at the moment and seems to be getting through his work so hopefully he will be fine too," McCullum said of Wood.
"We've still got a couple of days and will make the decision when we need to, but he seems to be progressing well."
All eyes were on captain Ben Stokes during England's training session on Monday.
There are doubts over how much he will bowl this summer following an Indian Premier League series where he only played twice and sent down just one over for Chennai Super Kings.
McCullum remains positive the talismanic all-rounder can still make an impact with the ball.
Asked if Stokes will bowl against Ireland, McCullum responded: "I don't know. You'll have to ask Stokesy. He's progressing well too.
"He looks really fit as well, looks in great order and has a big smile on his face.
"He is delighted to be back around the group and as our leader, having that sort of energy he brings is fantastic so again we'll monitor that and see what happens.
"I think he'll bowl at some stage throughout the summer, yeah, no doubt.
"He is a world class all-rounder and if he is able to bowl, fantastic. If not, we'll find a way."