Craig Gordon has said he will consider his Hearts future if the club receives a satisfactory offer for his services.
Gordon has been linked with several Premiership clubs
Sunderland had a recent £5m bid turned down for the Scotland goalkeeper, with the Tynecastle side's valuation of Gordon in the region of £10m.
"There's still a lot of time left in the transfer window so I might leave before the start of the season," Gordon told Hearts World.
"But I can't think about it much as I need to be ready for the new season."
Hearts begin their Premier League campaign on 6 August with an Edinburgh derby against Hibernian, and club captain Gordon is trying to keep his mind off the speculation surrounding him.
"It's out of my hands at the moment and we'll need to see what happens over the next few weeks," added the 23-times-capped keeper.
Fulham and Manchester United were also linked with moves for the 24-year-old earlier this year.
Gordon began his career in the Hearts youth team and is now firmly established as first choice for club and country.
And following the bid from Roy Keane's Black Cats, he admits a club of that stature would tempt him.
"That bid hasn't been accepted. If it had, I'd have to give it serious consideration.
"As yet there's not been a bid accepted from anybody, so I've got nothing to think about other than getting ready for the start of the season with Hearts and playing to the best of my ability."