Fletcher, 21, joined West Ham on a free transfer last summer following his release from Manchester United, signing a four-year contract at the London Stadium.
The Englishman made 19 appearances for the Hammers during the 2016-17 campaign, but he only started twice in the Premier League after struggling to break into the first-team picture.
The arrivals of Javier Hernandez and Marko Arnautovic have led to suggestions that Fletcher will depart this summer, and according to The Sun, Middlesbrough are in talks with West Ham over a £7m deal.
The report adds that Fletcher will fly home from West Ham's Germany training camp to begin talks with Garry Monk's team, who were relegated from the Premier League last season.
Fletcher only managed one goal for West Ham last season, but he netted nine times during a loan spell with Barnsley during the 2015-16 campaign.