Fletcher, 19, made his debut in the Carling Cup game against Morecambe in August, coming on as a substitute for Rodriguez.
With Rodriguez having become an increasingly influential member of Laws' squad, hopes are high at Turf Moor that Fletcher can follow suit.
"Wes impressed me in pre-season, hence my thoughts on including him in the squad over the summer, and he did really well with us," said Laws.
"He's strong, he's worked extremely hard on the physical side of things and he's got an eye for goal.
"He's a very quiet lad - he's like a Mark Hughes, quiet off the pitch, but not on it - but he's getting on with it and he's impressed us all. Is he another Jay? Let's hope so, he's got the potential to be."