The city is hoping to begin work this fall on the construction of a multipurpose athletic field on a portion of Whispering Hills, the 74.4-acre site west of Cambridge Road that Woburn purchased from Northeastern University in 2010. Weston & Sampson, the city’s engineering consultant on the project, is finalizing a design of the field, which the city intends to build on the lower, flat portion of the property closest to Cambridge Street, according to Mayor Scott D. Galvin. City officials were scheduled to solicit feedback from neighbors on the design at a community meeting last Wednesday  and are set to seek approval of the project from the Conservation Commission later this month. Should it receive that approval, the city would advertise construction bids with the hope of having a contractor ready to begin work in November. Woburn purchased the land for $6.7 million with the help of a $500,000 state grant. The city received a second $500,000 state grant last year, which it plans to use together with $370,000  in local funds authorized by the City Council to build the field.