Beckford's first-half winner against Premier League champions United was his 20th goal of the season, but with his contract due to run out in the summer, Grayson admits that Leeds will not stand in the player's way if they receive a substantial offer during January.
Grayson said: 'There has been speculation about Newcastle and Beckford, but my best case scenario is that Jermaine signs a new contract or gets us the goals to earn promotion and then leaves.
'We have stressed that there will be three scenarios with Jermaine. He signs a new contract, he leaves at the end of the season or we sell him and get some money which we think is too good an opportunity to turn down.
'Strikers are a precious commodity and we won't be letting him go on the cheap. That is the scenario we are going to go down.
'He has shown today what he is all about. He has worked ever so hard for the team and he has taken his opportunity.
'Money talks with any player, but we are not looking to sell him. People can speculate about him and we knew that, as soon as the window opened, there would be talk about him.
'We have made a decent amount of money today and got back on an even keel on the financial front, so we don't want him to leave unless it is something that suits him and the club.'
Beckford's goal erased Brian Flynn from the Leeds record books as the last man to score a winner for the club against United at Old Trafford.
But despite Beckford's personal achievement, Grayson insisted that his team's victory was down to more than one player.
He said: 'I told the players that, if you can perform at Old Trafford, somebody will be a hero.
'Everybody talked about Brian Flynn and he reminded me that he was the last player to score a winner at Old Trafford in 1981 when I saw him recently.
'Jermaine Beckford will get the credit now, but we are immensely proud of our team and what they have done today.
'We knew it would be difficult coming to Old Trafford, but we told the players to do themselves justice and be proud of themselves, whether they came back to the dressing room with a win, defeat or draw. They certainly did that.
'United have fantastic players, but we had a plan to contain them. We knew that we could deny them possession and that we had people who, when we had possession of the ball, could hurt them.'
From goalkeeper Casper Ankergren through to Beckford, Leeds outfought United throughout and Grayson confessed that his team were rarely troubled by Ferguson's men.
He said: 'Our keeper made some good saves, but he was not being peppered on a regular basis.
'He did what he had to do because he had players in front of him defending properly and making tackles.
'Our club has had a lot of negativity over the last five or six years with administration and relegation, so this is a result for our fans.
'Leeds is a big club. We are known in Europe and worldwide for our achievements in the 1960s and 70s, but we are in League One for a reason.
'I want to be back here managing this club in the Premier League, though, and we have to go through the Championship first to do that.'