Becchio made it 40 league goals in 89 starts for the club with his late double but is out of contract at the end of the season.
Grayson is keen to keep hold of the Argentinian and believes he will remain part of the squad.
He said: "Luciano Becchio is a fantastic player who has proved his worth to the club in terms of his goals and the effort he puts in for the team.
"That is why we are doing all we can to keep him.
"People probably under-estimate what he does for the team. He has scored a lot of goals this time and I am sure scouts will be taking notice of him but we want to keep our best players and there are not many bigger clubs than Leeds United in the Championship.
"Contract talks with Luciano are on-going but he has said he wants to stay.
"We plucked him from the third division of the Spanish League and helped to make him a better player so you hope for some loyalty from players in return."