Forest had a £1.5m bid rejected in January but have been heavily linked with a new improved bid in recent days.
That has intensified since James Perch left the City Ground for newly promoted Premier League side Newcastle United.
"There's obviously speculation but we haven't received any further approach from Nottingham Forest," said Swansea chairman Huw Jenkins.
"Looking in the papers, it seems they may be coming back in with an offer."
London-born Pratley was Swansea's top scorer last season with seven goals and has made 158 league and cup appearances since arriving from Fulham for £100,000 in June 2006.
Losing the 25-year-old would be a hammer blow for the Swans who have already seen another key midfielder leave this summer.
Leon Britton quit the Liberty Stadium on a free transfer to Sheffield United after a seven-year stay in south Wales.
But the difference with Pratley is that, unlike Britton, he is still under contract and the Swans do not need to sell players.
Jenkins has demonstrated this in the past by holding on to midfielder Ferrie Bodde last summer, rejecting bids of up to £5m from Wigan Athletic.
Forest boss Billy Davies is a keen admirer of Pratley and could choose to make a move while there is uncertainly over the vacant manager's job at Swansea, following Paulo Sousa's departure to Leicester City.
Source: BBC Sport
Source: BBC Sport