The goalkeeper has been one of the club's leading lights since joining the club in 2007, having been watched by several scouts in recent times after several outstanding performances between the sticks.
The 27-year-old has been linked with a move to Burnley to be reunited with former Owls boss Brian Laws, as well as Premier League outfits West Bromwich Albion and Wigan.
However Grant, who was voted Wednesday's player of the season, maintained that he wanted to stay at Hillsbrough despite their relegation to League One after failing to beat Crystal Palace in a dramatic 2-2 draw that condemned them to the third tier.
"As far as I am concerned, I've still got two more seasons on my contract so until someone tells me otherwise that is what I will be concentrating on," Grant told The Sheffield Star.
"I am fully focused on getting fit and ready to play a big part in a winning team next year.
"I'm concentrating on getting ready for pre-season training and leading the charge in League One."
With the Owls desperate to hold on to their star player, Grant maintained that he was in no rush to depart South Yorkshire and that speculation linking him with a move away was all part of football.
"There will be no transfer requests or sulking from me," he added.
"I will be getting on with the job at hand like anybody else and trying to put things right because I think as a squad we owe that to the supporters.
"The speculation is part of the game.
"It is obvious that there are going to have to be some changes somewhere along the line at the club and we have already seen that with some of the players who have gone."