Fletcher is aiming to secure a month-long deal after holding talks with the Glovers on Thursday.
The 22-year-old has been limited to just two senior appearances for Burnley since emerging from the club's youth team.
Fletcher has already gained Football League experience during loan spells at Crewe, Accrington Stanley, Stockport and Grimsby.
A statement from Burnley read: "Wes Fletcher is set to celebrate his birthday with a loan move to League One promotion chasers Yeovil Town.
"The Clarets' frontman is travelling to the West Country with a view to completing a deal running for an initial month."