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In the weeks ahead, Leeds also hope to agree new contracts with a number of the players whose deals are edging towards expiry.
Patrick Kisnorbo, Neil Kilkenny, Richard Naylor and Luciano Becchio are among those who, as things stand, would be available on free transfers next summer and Grayson is keen to tie down the members of his squad who played influential parts in the club's promotion from League One.
United are awaiting Hughes's response to their contract offer and the club have not ruled out the possibility that some of the players who finished the season on loan at Elland Road could return before the new Championship term begins.
Midfielder Michael Doyle is likely to be free to a move from Coventry City despite being under contract at the Ricoh Arena and Preston North End would not block an approach from Grayson for Scottish centre-back Neill Collins.
Shane Lowry has agreed a new two-year deal with Aston Villa and Gary McSheffrey is a free agent after Birmingham City turned down an option to extend his contract at St Andrews for a further two seasons.
Grayson said: "We'll be looking to extend the term of a number of the existing players' contracts and also make a decision on those players who have returned to their clubs having been here on loan."