The Bolton News says the midfielder helped the Welshmen beat Reading 4- 2 in Monday's play-off final at Wembley to return to the top flight for the first time in 28 years.
Pratley is out of contract in the summer after failing to agree a new deal to stay at the Liberty Stadium.
Owen Coyle is a huge fan of goalscoring 26-year-old, who he has tracked for the last 12 months, and is leading the race to sign him.
But the Swans' historic achievement in becoming the first Welsh club to reach the Premier League - and subsequent £90million cash boost - could put the move in jeopardy.
The Bolton boss, however, is hopeful that the box-to-box midfielder's future still lies at the Reebok.