The Edinburgh club are determined that the 22-year-old winger will not leave for anything below market value following an offer from Burnley plus inquiries from Chelsea, Wigan, Middlesbrough and FC Twente.
Burnley are interested in a potential 3million deal, comprising an initial 1.5million and the remainder in add-ons. However, Hearts director Sergejus Fedotovas has informed Driver's suitors that any primary payment must be in the region of 3.5m.
Chelsea's interest was revealed by the Evening News last week and is being dealt with solely by Romanov. He and Abramovich are close friends and discussions remain ongoing over a loan agreement for the player, which would include the option of a 5million purchase thereafter.
"We absolutely know what we want to achieve," said Fedotovas. "We have had a number of discussions with a few clubs and I'm glad we have been getting very healthy interest in the player. If we get a proposal which falls within our expectations then we will consider it very seriously. If not, then we will keep the player for the benefit of the team. To a larger extent, the interests of the player and the club coincide – for us to achieve a sizeable transfer fee and the player to get to a higher level to continue his development would be quite important."
Meanwhile, it was reported today that Rangers are hoping to meet with Jose Goncalves and his agent this week over a possible move to Ibrox. The 24-year-old defender's contract at Tynecastle expired at the end of the season.