And Grayson said: "It would have to be a lot of money because we have turned down decent money already for him.
"If someone comes in with ridiculous money - and I'm talking a lot more than £2m - then we'd look at it again."
Beckford scored a stoppage-time penalty for League One Leeds to cap a sensational FA Cup tie at White Hart Lane.
Tottenham, who are 41 league places above their opponents, looked set for victory when substitute Roman Pavlyuchenko had put the home side 2-1 ahead with 15 minutes remaining.
It was Beckford who had earlier cancelled out Peter Crouch's close-range opener with a typical poacher's effort minutes into the second half.
The striker has certainly made an impact in this season's FA Cup as it was his winning strike at Old Trafford which knocked Manchester United out in the third round.
Grayson, however, was adamant that he would do all that he could to prevent the striker from leaving in the January transfer window.
"I've got no intention of selling him in the window because it's too late to get a replacement and he's too valuable to lose," added Grayson.
"I have said all along I would rather Jermaine leave on a free and I wish him well because hopefully in that meantime he's got us promoted.
"Jermaine can only win because if he scores 15 to 20 goals until the end of the season he will be linked with bigger clubs than he's being linked with now."
The striker is already believed to have caught the eye of several Championship sides, but Grayson has not given up hope of securing the striker on a long-term deal.
"There's still an opportunity he might stay beyond the summer," added the Leeds boss, whose side are on course for promotion to the Championship.
"There have been a lot of twists and turns already. He put a request in after the Manchester United game and has come off the list now. He can leave in the summer if that's his choice."
Tottenham manager Harry Redknapp had no qualms with referee Alan Wiley's decision to award Leeds the penalty for Dawson's foul on Beckford.
"It could have been a penalty. It was a tight one. I wouldn't argue with the referee. He's made an honest decision. Sometimes you get them and sometimes you don't," said Redknapp.
"Michael took a chance and tried to win the ball. He did get a foot on the ball.
I don't think there is any shadow of a doubt that this Leeds team would more than hold its own in the Premiership clarkeyking "At that stage in the game we really should have killed the game off, we were running through trying to score again instead of playing it wide and keeping the ball.
"You can't get carried away with everybody wanting you to score again, you've got to make sure you win the game. We showed a lack of experience in not doing that."
Redknapp added that there were no imminent plans for goalscorer Pavlyuchenko to leave White Hart Lane.
The Russian, who came on as substitute to immediate effect, has been a peripheral figure this season and is believed to be looking for a move away from north London.
But Redknapp said: "Pav is here, he's part of the squad and if he plays like he did when he came on every week he will be in the team every week.
"It's up to him, if he wants to play and comes in every day willing to work and shows a good attitude there's every chance for him. It's up to him.
"It's like everybody, you have to earn the right to play and if he does that I haven't any problems. There's nothing in the offing."