Gray, 25, originally had until Wednesday, 31 August to reply to the Football Association, but was given an extension until Monday.
One of the tweets, posted when Gray was playing for non-league Hinckley United, appeared to condone killing gay people.
Premier League side Burnley said no date has yet been set for the hearing.
Gray, who is charged with bringing the game into disrepute, has apologised and asked "for forgiveness", insisting he is now a "completely different person" and does not "hold the beliefs written in those tweets".
The posts, which also contained offensive terms, were deleted soon after being highlighted.
Gray remains available to play for Burnley, who host Hull in the Premier League at 15:00 BST on Saturday.
Subscribe to the BBC Sport newsletter to get our pick of news, features and video sent to your inbox.
Burnley striker Andre Gray has asked for a personal hearing over his misconduct charge for homophobic posts on Twitter in 2012.