Fletcher has played Andy Sugden in the long-running ITV show since 1996.
Producers said they would not confirm or deny the reports.
A statement said: “We do not comment on the cast contracts nor future storylines.”
The 32-year-old actor is said to be leaving to pursue a career as a racing driver, according to The Sun.
Fletcher has to date competed in numerous sporting events including the 2016 British Touring Car Championship and the Porsche Carrera Cup.
His character arrived in the soap as Andy Hopwood, but was adopted by Jack and Sarah Sugden, and so became a permanent part of the Sugden family.
Well-known storylines over the years include Andy setting fire to the farm’s barn, as well as a domestic abuse storyline and a plot which saw his brother Robert being shot.
Currently Andy is on trial for the shooting of Lawrence White and viewers are waiting to see if he will be convicted for the crime, which he did not commit.
Fletcher’s publicist has been contacted for comment.