Burnley boss Brian Laws has asked Wolves about young Wales international Wayne Hennessey and Newcastle about Forster.
Forster is also wanted at Norwich City next season, after being named their players' player of the year.
The 22-year-old made 42 appearances for the Canaries, in all competitions, keeping 21 clean sheets - including four in a row at the end of the season as Norwich clinched an immediate return to the Championship by winning the League One title.