Considerations for planting cover crops after wheat in grain crop rotations are common this point in the season. With any cover crop, it is advisable to select a species with a given target in mind (surface erosion prevention, nutrient scavenging, N fixation, soil coverage, etc.).
Grass species, like oats or ryegrass, are typically fast to establish and can provide soil coverage to reduce erosion. Some species (like oats) will typically winterkill, whereas other species are more hardy and may need to be controlled in the spring before or shortly after planting. Additionally, some grass species may be alternate hosts for some corn pests (fungal diseases, nematodes) and may not be the best choice to follow wheat and precede corn in the rotation.
Some legume species (like vetches and crimson clover) may be able to tolerate August weather well if temperatures stay on the cooler side of average. These could provide N to corn next year if inoculated with rhizobia prior to planting, but may serve as an alternate host for soybean cyst nematode and should be avoided if soybeans are planned for next year. Other legumes (most other clovers) are poor hosts for soybean cyst nematode and could be a better option if rotating to soybean. Field pea may be another option as a legume, but if seeded in August it may not overwinter as compared to a mid-September seeding.
Brassica species (like tillage radish) will establish well and help reduce winter annual weed populations if seeded early, and should produce large taproots to help aerate the soil. Because precipitation and temperatures can be variable this time of year, the use of a cover crop mixture may be advantageous to ensure at least one species succeeds in establishing in the field.
Cover crops after winter wheat can also be a source of forage for producers with livestock. Excellent options for August to early September plantings include oat, spring triticale, Italian ryegrass, forage brassicas (early August plantings and for grazing only). Be aware that Italian ryegrass can become a weed problem in grain crop rotations, so it may not be desirable where grain production is the main objective for the land.
(Source – http://ocj.com/2017/08/cover-crops-following-wheat/)