Reid had hoped to play the 23-year-old against Aston Villa and Shelbourne but although he was unable to make the trip, the Elland Road boss is still confident of a move.
"Colin will train with us on Monday and Tuesday. We are interested in him and I have spoken to Martin O'Neill but what was said will remain between us," said Reid.
Healy is out of contract at Parkhead, but as he is under 24, Leeds would have to pay compensation if they wanted to make the deal permanent.
The Irish international has become disillusioned with life at Parkhead as he has failed to hold down a first-team place in Martin O'Neill's side and he could be The Whites' fourth capture of the pre-season.
Reid's old club Sunderland were also interested but could not afford the settlement.