If you do enough jogging, it will help your mile time. But, progress will be slow. It's not likely jogging, by itself, will improve your mile time by 1.5 to 2.5 minutes in 2 months.
To improve your mile time, you want to do some workouts that have parts where you run faster than your mile pace. A common workout for this is intervals. You might, for example, warm up, and then alternate 200 meter sprints with walking rest periods. Each week, you would increase the number of intervals.
You can do a web search for "mile training plan."