Hearts are willing to listen to offers of £3 million for captain Christophe Berra.
The Daily Mail says agents acting on behalf of Berra have been given the green light to source buyers.
Although English Premier League sides might not be convinced at the asking price, a down payment of around £2m plus additional installments could tempt Vladimir Romanov to sell.
Fulham, Everton and Bolton have all made recent checks on Berra and winger Andy Driver, but the Goodison club's idea of a loan until the summer is not attractive to the Hearts hierarchy.
"Berra is a good player and everyone knows about him - but a lot could depend on what is the asking price," said Fulham boss Roy Hodgson on Friday night.