The 34-year-old marathon world record holder is recovering from a stress fracture to her left thigh which threatens her participation.
But Collins said: "I think there is a progression we'd hope to see and that was laid down in the original plan.
"All the reports I am getting is that she is on schedule...
Last month Radcliffe said she was determined to make the Olympics, despite medical advice claiming the injury would make it impossible for her to achieve full fitness in time.
Since learning of the injury, Radcliffe has returned to her training base at Font Romeu in the French Pyrenees in a bid to make a fourth successive Olympic appearance.
Collins is closely monitoring the situation and added: "It's a significant injury and certainly she's been very committed and worked well.
"She's in the pool and cross training but not actually running. As you would expect from an athlete committed to putting herself on the start line, we will give her all the help we can."
Collins suggested they will wait until 20 July, when the final British team is announced, before making a decision on Radcliffe.
"I would want to give her as much time as possible to see if she is capable of taking her place," he added.
Radcliffe has been selected for Team GB along with Liz Yelling and Mara Yamauchi, with Hayley Haining waiting in the sidelines should be forced to withdraw.