Yes, there may be deposits of manganese in the ophiolite. The ophiolite is a sequence of rocks that includes several types of rocks which may contain certain minerals, including manganese. Manganese is considered a common element in some sedimentary sequences associated with granite, as mentioned in some research. Therefore, it is possible for manganese to find its way into these geological formations.
Manganese nodules are commonly formed on ocean floors in divergent plate tectonic environments. Ophiolites are formed through transportation of oceanic floor material over periods of millions of years and then scrapped off from the top of the oceanic slab at a subduction zone and eventually deposited or dumped on to continental environments. This is the same mechanism by which cyprus type massive sulphide deposits are formed. It is therefore reasonable to expect manganese deposits to occur in ophiolites. Many such case deposits are highlighted if you google “manganese deposits in ophiolites”.