Fletcher celebrates after leading Barnsley to victory at Wembley
Keighley-born Fletcher spent the latter half of last season on loan to the Tykes from Manchester United, and fired the South Yorkshire side to promotion via the League One play-offs.
According to reports at the weekend, the 20-year-old caught the eye of Leeds owner Massimo Cellino during last month's 3-1 win against Millwall at Wembley.
Fletcher fires the Tykes ahead against Millwall
"Barnsley is now a club that I hold very deep in my heart, and it would be an option if United did send me out on loan again," Fletcher is quoted as saying.
"I have thoroughly enjoyed my time here and loved every minute of it."
He added: "Coming to Barnsley has been a great move for my career. There is a real bond in the dressing room and I think you have seen that in the performances on the pitch since January."
Fletcher scored nine goals in 26 appearances for Barnsley, and could fill the void left by Mirco Antenucci at Elland Road.
Antenucci's exit has left Leeds short of strikers
The Italian was released at the end of last season, leaving the Whites with only Chris Wood and Souleymane Doukara as recognised centre forwards.
However, Fletcher's future could hinge on that of Heckingbottom, who is expected to hold talks to turn his temporary contract permanent this week.
Heckingbottom (L) has been in caretaker charge since February