Harkalm Investments lodged the plan on behalf of the multi-national coffee chain which would see the shop built opposite the Hammer and Pincers car park, next to The Chain Bridge, in Swineshead Road.
As part of the plan, a drive-thru outlet would be built along with 19 car parking spaces and two electric vehicle charging points.
The company said in its plans that the shop would create new jobs and would ‘not detract from the viability and vitality’ of the town centre.
A total of 13 full time and 22 part time jobs would be created at the shop, according to the proposals.
Boston Borough Council will make a decision on the plan at a later date.
The news follows similar proposals for drive-thru coffee shops, fast-food restaurants and homes at the town’s Quadrant scheme.
Councillors gave the go-ahead for the fifth phase of the project last September, which will see 68 new homes built.
Elsewhere on the development, Travelodge has also applied to vary its build. The company wants to increase the number of rooms from 52 to 56.
When complete, The Quadrant scheme will eventually comprise 500 homes, a series of commercial premises, and a new stadium for Boston United Football Club.